View source for Cosmic inflation

{{Short description|Theory of rapid universe expansion}}
{{Redirect2|Inflation model|Inflation theory|a general rise in the price level|Inflation|other uses|Inflation (disambiguation)}}
{{Use dmy dates|date=July 2019}} 
{{Cosmology|early}}
In [[physical cosmology]], '''cosmic inflation''', '''cosmological inflation''', or just '''inflation''', is a theory of exponential [[expansion of the universe|expansion of space]] in the very early [[universe]]. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due to [[dark energy]] began after the universe was already over 7.7&nbsp;billion years old (5.4&nbsp;billion years ago).<ref>{{cite serial |title=[[How the Universe Works#Season 3|How The Universe Works 3]] |episode=First Second of the Big Bang |network=Discovery Science |year=2014}}</ref>

Inflation theory was developed in the late 1970s and early 1980s, with notable contributions by several [[theoretical physics|theoretical physicists]], including [[Alexei Starobinsky]] at [[Landau Institute for Theoretical Physics]], [[Alan Guth]] at [[Cornell University]], and [[Andrei Linde]] at [[Lebedev Physical Institute]]. Starobinsky, Guth, and Linde won the 2014 [[Kavli Prize]] "for pioneering the theory of cosmic inflation".<ref name=KavliPrize>{{cite web |title=2014 Astrophysics Citation |url=http://www.kavlifoundation.org/2014-astrophysics-citation |website=The Kavli Foundation |access-date=27 July 2014 |archive-date=14 July 2014 |archive-url=https://web.archive.org/web/20140714114045/http://www.kavlifoundation.org/2014-astrophysics-citation }}</ref> It was developed further in the early 1980s. It explains the origin of the [[Observable universe#Large-scale structure|large-scale structure of the cosmos]]. [[Quantum fluctuation]]s in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see [[galaxy formation and evolution]] and [[structure formation]]).<ref>Tyson, Neil deGrasse and Donald Goldsmith (2004), ''Origins: Fourteen Billion Years of Cosmic Evolution'', W. W. Norton & Co., pp. 84–85.</ref> Many physicists also believe that inflation explains why the universe appears to be the same in all directions ([[isotropic]]), why the [[cosmic microwave background]] [[radiation]] is distributed evenly, why the universe is [[flat universe|flat]], and why no [[magnetic monopole]]s have been observed.

The detailed [[particle physics]] mechanism responsible for inflation is unknown. A number of inflation model predictions have been confirmed by observation; for example temperature anisotropies observed by the COBE satellite in 1992 exhibit nearly scale-invariant spectra as predicted by the inflationary paradigm and [[WMAP]] results also show strong evidence for inflation.<ref>
{{cite arXiv
 |author=Tsujikawa, Shinji
 |date=28 April 2003
 |title=Introductory review of cosmic inflation
 |eprint=hep-ph/0304257
}}
</ref> However, some scientists dissent from this position.<ref name=Steinhardt2011/><ref name="Earman-Mosterín"/><ref name="Hložek"/> The hypothetical [[field (physics)|field]] thought to be responsible for inflation is called the [[inflaton]].<ref>{{cite book |author=Guth, Alan H. |author-link=Alan Guth |year=1997a |title=The Inflationary Universe: The quest for a new theory of cosmic origins |publisher=Basic Books |isbn=978-0-201-32840-0 |pages=[https://archive.org/details/inflationaryuniv0000guth/page/233 233]–234 |url=https://archive.org/details/inflationaryuniv0000guth |url-access=registration }}</ref>

In 2002, three of the original architects of the theory were recognized for their major contributions; physicists [[Alan Guth]] of [[Massachusetts Institute of Technology|M.I.T.]], Andrei Linde of [[Stanford]], and [[Paul Steinhardt]] of [[Princeton University|Princeton]] shared the [[Dirac Medal (ICTP)|Dirac Prize]] "for development of the concept of inflation in cosmology".<ref name= "Dirac Prize" >{{cite web |title=The Medallists: A list of past Dirac Medallists |website=ictp.it  |url=https://www.ictp.it/about-ictp/prizes-awards/the-dirac-medal/the-medallists.aspx}}</ref> In 2012, Guth and Linde were awarded the [[Breakthrough Prize in Fundamental Physics]] for their invention and development of inflationary cosmology.<ref name= "Breakthrough Prize" >{{cite web |title=Laureates of the Breakthrough Prize in Fundamental Physics in 2012 |website=breakthroughprize.org |publisher=[[Breakthrough Prize in Fundamental Physics]] |url=https://breakthroughprize.org/Laureates/1/P1/Y2012}}</ref>

== Concept ==
[[File:Big bang inflation vs standard genericchart.png|thumb|Exponential inflation very early in the universe matches observations better than extrapolations of Big Bang based models.]]
Cosmic inflation is the hypothesis that the very early universe expanded exponentially fast. Distances between points doubled every 10<sup>-37</sup> seconds; the expansion lasted at least 10<sup>-35</sup> seconds, but its full duration is not certain.  All of the mass-energy in all of the galaxies currently visible started in a sphere with a radius around 4 x 10<sup>-29</sup>&nbsp;m then grew to a sphere with a radius around 0.9&nbsp;m by the end of inflation.<ref name=Ryden-2016>{{Cite book |last=Ryden |first=Barbara |url=https://www.cambridge.org/core/product/identifier/9781316651087/type/book |title=Introduction to Cosmology |date=2016-11-17 |publisher=Cambridge University Press |isbn=978-1-107-15483-4 |edition=2 |doi=10.1017/9781316651087}}</ref>{{rp|202}} At the end of inflation the driving field converts to particles, leading to a quark-soup phase of the universe, a phase that retains small density variations due to quantum fluctuations in the original small smooth patch of the universe.<ref name=TurnerPrecision>{{Cite journal |last=Turner |first=Michael S. |date=2022-09-26 |title=The Road to Precision Cosmology |url=https://www.annualreviews.org/doi/10.1146/annurev-nucl-111119-041046 |journal=Annual Review of Nuclear and Particle Science |language=en |volume=72 |issue=1 |pages=1–35 |doi=10.1146/annurev-nucl-111119-041046 |issn=0163-8998|arxiv=2201.04741 |bibcode=2022ARNPS..72....1T }}</ref>

==Motivations==
Inflation resolves [[Big Bang#Problems and related issues in physics|several problems]] in [[Big Bang]] cosmology that were discovered in the 1970s.<ref>Much of the historical context is explained in {{harvp|Peebles|1993|at=ch&nbsp;15–17}}.</ref> The Big Bang model successfully explained the [[cosmic microwave background]] and [[Big Bang nucleosynthesis|synthesis]] of primordial elements. However these successes relied on assuming initial conditions that were difficult to justify. For example, the model has no mechanism to create density fluctuation which could explain the [[structure formation|formation of galaxies]].<ref name="peacock"/>{{rp|324}} When particle physicists took up the problem of the very early universe they immediately found additional problems.<ref name="Smeenk-2018">{{Cite book |last=Smeenk |first=Chris |chapter-url=https://doi.org/10.1007/978-1-4939-7708-6_9 |title=Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology in the Twentieth Century |date=2018 |publisher=Springer |isbn=978-1-4939-7708-6 |editor-last=Rowe |editor-first=David E. |location=New York, NY |pages=205–241 |language=en |chapter=Inflation and the Origins of Structure  |series=Einstein Studies |volume=14 |doi=10.1007/978-1-4939-7708-6_9 |editor-last2=Sauer |editor-first2=Tilman |editor-last3=Walter |editor-first3=Scott A.}}</ref> Inflation was first proposed by particle physicist Alan Guth in 1979 while investigating the problem of why no [[magnetic monopoles]] are seen today; he found that a positive-energy [[false vacuum]] would, according to [[general relativity]], generate an exponential expansion of space. The expansion also resolves other long-standing problems including the flatness problem and the horizon problem as discussed below.

=== Structure formation ===
{{main| Structure formation}}
The Big Bang theory postulates an initial very hot uniform plasma that expands according to the equations of general relativity and ultimately produces all of the stars and galaxies. The production of stars assumes that gravity causes mass to clump, but this requires density contrast: a completely uniform mass density has no force to drive clumping. Statistical variations in density would provide the force, but expansion of the universe works faster, pulling the mass apart before it can concentrate into a star. Without an additional source of variation, Big Bang models could not produce stars.<ref name=Smeenk-2018/>{{rp|207}}

===Magnetic-monopole problem===
{{main| Big Bang#Magnetic monopoles}}

Stable magnetic monopoles are a problem for [[Grand Unified Theory|Grand Unified Theories]], which propose that at high temperatures (such as in the early universe), the [[electromagnetic force]], [[strong nuclear force|strong]], and [[weak nuclear force|weak]] [[nuclear force]]s are not actually fundamental forces but arise due to [[spontaneous symmetry breaking]] from a single [[gauge theory]]. These theories predict a number of heavy, stable particles that have not been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "charge" of magnetic field.<ref>
{{cite journal
 |last='t Hooft |first=Gerard  |author-link=Gerard 't Hooft 
 |year=1974
 |title=Magnetic monopoles in unified gauge theories
 |journal=[[Nuclear Physics B]]
 |volume=79  |issue=2  |pages=276–84
 |bibcode=1974NuPhB..79..276T  |hdl=1874/4686  |doi=10.1016/0550-3213(74)90486-6
 |url=http://dspace.library.uu.nl:8080/handle/1874/4686
|archive-url=https://web.archive.org/web/20241204020241/http://dspace.library.uu.nl:8080/handle/1874/4686
|archive-date=4 December 2024
}}

</ref><ref>
{{Cite journal
 |first=Alexander M. |last=Polyakov
 |year=1974
 |title=Particle spectrum in quantum field theory
 |journal=[[JETP Letters]]
 |volume=20 |pages=194–195
 |bibcode=1974JETPL..20..194P
}}
</ref>

Monopoles are predicted to be copiously produced following Grand Unified Theories at high temperature,<ref>
{{Cite journal
 |first1=Alan |last1=Guth  |author-link=Alan Guth
 |first2=S.   |last2=Tye
 |year=1980
 |title= Phase transitions and magnetic monopole production in the very early universe
 |journal=[[Physical Review Letters]]
 |volume=44  |issue=10  |pages=631–635; Erratum ''ibid.'' (1980) '''44''' p&nbsp;963
 |doi=10.1103/PhysRevLett.44.631
 |bibcode=1980PhRvL..44..631G  |osti=1447535
 |url=http://repository.ust.hk/ir/bitstream/1783.1-49322/1/PhysRevLett.44.631.pdf
 |url-status=live
 |archive-url=https://ghostarchive.org/archive/20221009/http://repository.ust.hk/ir/bitstream/1783.1-49322/1/PhysRevLett.44.631.pdf
 |archive-date=2022-10-09
}}
</ref><ref>
{{Cite journal
 |first1=Martin B. |last1=Einhorn
 |last2=Stein      |first2=D.L.
 |last3=Toussaint  |first3=Doug
 |year=1980
 |title=Are grand unified theories compatible with standard cosmology?
 |journal=[[Physical Review D]]
 |volume=21 |issue=12 |pages=3295–3298
 |bibcode=1980PhRvD..21.3295E |doi=10.1103/PhysRevD.21.3295
}}
</ref> and they should have persisted to the present day, to such an extent that they would become the primary constituent of the Universe.<ref>
{{Cite journal
 |first1=Ya.    |last1=Zel'dovich
 |first2=M. Yu. |last2=Khlopov
 |year=1978
 |title=On the concentration of relic monopoles in the universe
 |journal=[[Physics Letters B]]
 |volume=79  |issue=3  |pages=239–41
 |bibcode=1978PhLB...79..239Z  |doi=10.1016/0370-2693(78)90232-0
}}
</ref><ref>
{{cite journal
 |first=John |last=Preskill
 |year=1979
 |title=Cosmological production of superheavy magnetic monopoles |doi=10.1103/PhysRevLett.43.1365
 |journal=[[Physical Review Letters]]
 |volume=43 |issue=19 |pages=1365–1368
 |bibcode=1979PhRvL..43.1365P
 |url=https://authors.library.caltech.edu/6133/1/PREprl79.pdf
 |url-status=live
 |archive-url=https://ghostarchive.org/archive/20221009/https://authors.library.caltech.edu/6133/1/PREprl79.pdf
 |archive-date=2022-10-09 
}}
</ref> Not only is that not the case, but all searches for them have failed, placing stringent limits on the density of relic magnetic monopoles in the Universe.<ref>
{{Cite journal
 |last1=Yao |first1=W.-M.
 |display-authors=etal
 |collaboration=Particle Data Group
 |year=2006
 |title=Review of Particle Physics
 |journal=[[Journal of Physics G]]
 |volume=33 |issue=1 |pages=1–1232
 |arxiv=astro-ph/0601168 |bibcode=2006JPhG...33....1Y
 |doi=10.1088/0954-3899/33/1/001
 |s2cid=262936640
 |url=http://pdg.lbl.gov/
}}
</ref>

A period of inflation that occurs below the temperature where magnetic monopoles can be produced would offer a possible resolution of this problem: Monopoles would be separated from each other as the Universe around them expands, lowering their observed density by many orders of magnitude.<ref name="Ryden2003">{{cite book |author=Barbara Sue Ryden |title=Introduction to cosmology |date=2003 |publisher=Addison-Wesley |isbn=978-0-8053-8912-8}}</ref>{{rp|202}}

While solving the monopole problem motivated the original hypothesis, not every cosmologist was impressed. [[Martin Rees]] has written,
: "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100&nbsp;percent effective against a disease that doesn't exist!"<ref>
{{cite book
 |last=Rees |first=Martin  |author-link=Martin Rees
 |year=1998
 |title=Before the Beginning
 |place=New York, NY
 |publisher=Basic Books
 |page=185
 |isbn=0-201-15142-1
}}
</ref>
However, the flatness and especially the horizon problem are also solved by inflation theory.<ref name="Ryden2003"/>{{rp|202}}

===Flatness problem===
{{Main|Flatness problem}}
The '''flatness problem''' (also known as the '''oldness problem''') is a [[physical cosmology|cosmological]] [[Fine-tuned universe|fine-tuning]] problem within the [[Big Bang]] model of the universe. Observations of the cosmic microwave background have demonstrated that the Universe is [[Flatness problem#Flatness|flat]] to within a few percent.<ref>
{{cite web |title=WMAP – Content of the Universe |url=http://map.gsfc.nasa.gov/universe/uni_matter.html |website=nasa.gov}}
</ref> The [[expansion of the universe]] increases flatness. Consequently the early universe must have been exceptionally close to flat. 
In standard cosmology based on the [[Friedmann equations]] the [[density of the universe|density of matter and energy in the universe]] affects the curvature of space-time, with a very specific [[Critical density (cosmology)|critical value]] being required for a flat universe.<ref name="Lightman1993">
{{cite book
 |first=Alan P. |last=Lightman
 |title=Ancient Light: Our Changing View of the Universe
 |date=1 January 1993
 |publisher=Harvard University Press
 |isbn=978-0-674-03363-4
}}
</ref>{{rp|p=61}} The current density of the universe is observed to be very close to this critical value. Since any departure of the total density from the critical value would increase rapidly over [[cosmic time]],<ref name="peacock">{{cite book |last= Peacock|first=J. A. |title= Cosmological Physics |url= https://archive.org/details/cosmologicalphys0000peac|url-access= registration|date= 1998|publisher=Cambridge University Press |location=Cambridge |isbn= 978-0-521-42270-3}}</ref> the early universe must have had a density even closer to the critical density, departing from it by one part in 10<sup>62</sup> or less. This leads cosmologists to question how the initial density came to be so closely fine-tuned to this 'special' value.<ref name=Cox-2017>{{Cite book |last1=Cox |first1=Brian  |title=Universal: a guide to the cosmos |last2=Forshaw |first2=J. R. |date=2017 |publisher=Da Capo Press |isbn=978-0-306-82270-4 |edition=1 |location=Boston, MA |oclc=973019447}}</ref>{{rp|196}}

===Horizon problem===
{{Main |Horizon problem}}
The [[horizon problem]] is the problem of determining why the universe appears statistically homogeneous and isotropic in accordance with the [[cosmological principle]].<ref>{{cite journal |title=The isotropy of the universe |doi=10.1088/0264-9381/15/2/008 |first1=Charles W. |last1=Misner |date=1968 |journal=[[Astrophysical Journal]] |volume=151 |issue=2 |page=431 |last2=Coley |first2=A A |last3=Ellis |first3=G F R |last4=Hancock |first4=M |bibcode=1998CQGra..15..331W |s2cid=250853141 }}</ref><ref name="mtw">{{Cite book |last=Misner |first=Charles |author2=Thorne, Kip S. |author3=Wheeler, John Archibald |name-list-style=amp |title=Gravitation |url=https://archive.org/details/gravitation00whee |url-access=limited |location=San Francisco |publisher=W. H. Freeman |date=1973 |isbn=978-0-7167-0344-0 |pages=[https://archive.org/details/gravitation00whee/page/n521 489]–490, 525–526}}</ref><ref name="weinberg">{{Cite book |first=Steven |last=Weinberg |title=Gravitation and Cosmology |publisher=John Wiley |date=1971 |isbn=978-0-471-92567-5 |pages=[https://archive.org/details/gravitationcosmo00stev_0/page/740 740, 815] |url=https://archive.org/details/gravitationcosmo00stev_0/page/740 }}</ref> For example, molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. In the Big Bang model without inflation, gravitational expansion separates regions too quickly: the early universe does not have enough time to equilibrate. In a Big Bang with only the [[matter]] and [[radiation]] known in the Standard Model, two widely separated regions of the observable universe cannot have equilibrated because they move apart from each other faster than the [[speed of light]] and thus have never come into [[causal contact]].

== Theory ==
{{See also|Expansion of the universe}}
Each of the motivations for inflation are issues related to the initial conditions for the expansion of the universe. 
The inflation solution starts with a tiny universe in thermal equilibrium then expands it much faster than the speed of light, so fast that the equilibrated parts are widely separated by the time gravitational expansion takes over. The results is a homogeneous and isotropic universe as the initial conditions for the expansion predicted by general relativity.<ref name=Ryden-2016/>{{rp|202}}

The theory of inflation thus explains why the temperatures and curvatures of different regions are so nearly equal. It also predicts that the total curvature of a space-slice at constant global time is zero. This prediction implies that the total ordinary matter, [[dark matter]] and residual [[vacuum energy]] in the Universe have to add up to the [[Critical density (cosmology)|critical density]], and the evidence supports this. More strikingly, inflation allows physicists to calculate the minute differences in temperature of different regions from quantum fluctuations during the inflationary era, and many of these quantitative predictions have been confirmed.<ref name=wmap2>{{cite journal |last=Spergel |first=D. N. |year=2007 |title=Three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Implications for cosmology |url=http://lambda.gsfc.nasa.gov/product/map/current/map_bibliography.cfm |journal=[[The Astrophysical Journal Supplement Series]] |volume=170 |issue=2 |pages=377–408 |arxiv=astro-ph/0603449 |bibcode=2007ApJS..170..377S |citeseerx=10.1.1.472.2550 |doi=10.1086/513700 |s2cid=1386346 |archive-url=https://web.archive.org/web/20100924220120/http://lambda.gsfc.nasa.gov/product/map/current/map_bibliography.cfm |archive-date=24 September 2010 |access-date=10 October 2006 |quote=WMAP ... confirms the basic tenets of the inflationary paradigm&nbsp;... }}</ref><ref>{{cite news |title=Our baby universe likely expanded rapidly, study suggests |date=28 February 2012 |website=Space.com |url=http://www.space.com/14699-universe-inflation-cosmic-expansion-theory.html }}</ref>

===Space expands===
Looking backwards to smaller scales and higher energy in the very early universe eventually leads to a point where existing models may not be valid. There is no particular reason to expect normal physics to apply. The inflation hypothesis is that in this very early time space expands exponentially by many orders of magnitude.<ref name=Dodelson-2003>{{Cite book |last=Dodelson |first=Scott |title=Modern cosmology |date=2002 |publisher=Academic Press |isbn=978-0-12-219141-1 |edition=Nachdr. |location=Amsterdam}}</ref>{{rp|146}} 
In a space that expands exponentially (or nearly exponentially) with time, any pair of free-floating objects that are initially at rest will move apart from each other at an accelerating rate, at least as long as they are not bound together by any force. From the point of view of one such object, the spacetime is something like an inside-out [[Schwarzschild metric|Schwarzschild black hole]]—each object is surrounded by a spherical event horizon. Once the other object has fallen through this horizon it can never return, and even light signals it sends will never reach the first object (at least so long as the space continues to expand exponentially).

In the approximation that the expansion is exactly exponential, the horizon is static and remains a fixed physical distance away. This patch of an inflating universe can be described by the following [[metric tensor|metric]]:<ref>{{cite journal |last1=Melia |first1=Fulvio |year=2008 |title=The Cosmic Horizon |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=382 |issue=4 |pages=1917–1921 |doi=10.1111/j.1365-2966.2007.12499.x |doi-access=free |bibcode=2007MNRAS.382.1917M |arxiv=0711.4181 |s2cid=17372406 }}</ref><ref>{{cite journal |last1=Melia |first1=Fulvio |date=2009 |title=The Cosmological Spacetime |journal=[[International Journal of Modern Physics D]] |volume=18 |issue=12 |pages=1889–1901 |doi=10.1142/s0218271809015746 |display-authors=etal |bibcode=2009IJMPD..18.1889M |arxiv=0907.5394 |s2cid=6565101 }}</ref>

:<math>
ds^2=- (1- \Lambda r^2) \, c^2dt^2 + {1\over 1-\Lambda r^2} \, dr^2 + r^2 \, d\Omega^2.
</math>

This exponentially expanding spacetime is called a [[de Sitter space]], and to sustain it there must be a [[cosmological constant]], a [[dark energy|vacuum energy]] density that is constant in space and time and proportional to Λ in the above metric. For the case of exactly exponential expansion, the vacuum energy has a negative pressure ''p'' equal in magnitude to its energy density ''ρ''; the [[Equation of state (cosmology)|equation of state]] is {{nowrap begin}}''p=−ρ''{{nowrap end}}.

Inflation is typically not an exactly exponential expansion, but rather quasi- or near-exponential. In such a universe the horizon will slowly grow with time as the vacuum energy density gradually decreases.

===Few inhomogeneities remain===
Because the accelerating expansion of space stretches out any initial variations in density or temperature to very large length scales, an essential feature of inflation is that it smooths out [[homogeneity (physics)|inhomogeneities]] and [[anisotropy|anisotropies]], and reduces the [[shape of the universe|curvature of space]]. This pushes the Universe into a very simple state in which it is completely dominated by the [[inflaton]] field and the only significant inhomogeneities are tiny [[quantum fluctuation]]s. Inflation also dilutes exotic heavy particles, such as the [[magnetic monopole]]s predicted by many extensions to the [[Standard Model]] of [[particle physics]]. If the Universe was only hot enough to form such particles ''before'' a period of inflation, they would not be observed in nature, as they would be so rare that it is quite likely that there are none in the [[observable universe]]. Together, these effects are called the inflationary "no-hair theorem"<ref>{{harvp|Kolb|Turner|1988}}</ref> by analogy with the [[no hair theorem]] for [[black hole]]s.

The "no-hair" theorem works because the cosmological horizon is no different than that of a black-hole except in that there'd not be testable disagreements about what would be on the other side. One interpretation of the no-hair theorem is that the Universe (observable and unobservable) expands by an enormous factor during inflation. In an expanding universe, [[energy density|energy densities]] generally fall, or get diluted, as the volume of the Universe increases. For example, the density of ordinary "cold" matter (dust) declines as the inverse of the volume: when linear dimensions double, the energy density declines by a factor of eight; the radiation energy density declines even more rapidly as the Universe expands since the wavelength of each [[photon]] is stretched ([[redshift]]ed), in addition to the photons being dispersed by the expansion. When linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen (see [[Equation of state (cosmology)#Ultra-relativistic matter|the solution of the energy density continuity equation for an ultra-relativistic fluid]]). During inflation, the energy density in the inflaton field is roughly constant. However, the energy density in everything else, including inhomogeneities, curvature, anisotropies, exotic particles, and standard-model particles is falling, and through sufficient inflation these all become negligible. This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins.

===Reheating===
Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model-dependent, but in the first models it was typically from {{10^|27}}&nbsp;K down to {{10^|22}}&nbsp;K.<ref name=Guth-1982-NuffWksh>
{{cite conference
 |last=Guth |first=Alan
 |date=21 June – 9 July 1982
 |title=Phase transitions in the very early universe
 |editor1-last=Gibbons |editor1-first=G.W.
 |editor2-last=Hawking |editor2-first=S.  |editor2-link=Stephen Hawking
 |editor3-last=Siklos  |editor3-first=S.T.C. 
 |edition=illustrated, reprint
 |conference=The Very Early Universe: Proceedings of the Nuffield Workshop, [[Cambridge University|Cambridge]]
 |place=Cambridge, UK
 |publisher=[[Cambridge University Press|Cambridge U.P.]]
 |publication-date=29 March 1985
 |orig-date=1st ed. 1983
 |isbn=978-0-521-31677-4
 |oclc=14137101
}} {{ISBN|0-521-31677-4}}
</ref>) This relatively low temperature is maintained during the inflationary phase. When inflation ends, the temperature returns to the pre-inflationary temperature; this is called ''reheating'' or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with [[Standard Model]] particles, including [[electromagnetic radiation]], starting the [[radiation-dominated era|radiation dominated phase]] of the Universe. Because the nature of the inflaton field is not known, this process is still poorly understood, although it is believed to take place through a [[parametric oscillator|parametric resonance]].<ref>
See {{harvp|Kolb|Turner|1988}} or {{harvp|Mukhanov|2005}}.
</ref><ref>
{{cite journal
 |first1=Lev     |last1=Kofman
 |first2=Andrei  |last2=Linde
 |first3=Alexei  |last3=Starobinsky
 |year=1994
 |title=Reheating after inflation
 |journal=[[Physical Review Letters]]
 |volume=73  |issue=5  |pages=3195–3198
 |bibcode=1986CQGra...3..811K  |pmid=10057315
 |arxiv=hep-th/9405187  |s2cid=250890807
 |doi=10.1088/0264-9381/3/5/011
}}
</ref>

==History==

===Precursors===
In the early days of [[General Relativity|general relativity]], [[Albert Einstein]] introduced the [[cosmological constant]] to allow a [[Einstein static universe|static solution]], which was a [[3-sphere|three-dimensional sphere]] with a uniform density of matter. Later, [[Willem de Sitter]] found a highly symmetric inflating universe, which described a universe with a cosmological constant that is otherwise empty.<ref>
{{Cite journal
 |first=Willem |last=de Sitter
 |year=1917
 |title=Einstein's theory of gravitation and its astronomical consequences. Third paper
 |journal=[[Monthly Notices of the Royal Astronomical Society]]
 |volume=78 |pages=3–28
 |bibcode=1917MNRAS..78....3D
 |doi=10.1093/mnras/78.1.3 |doi-access=free
}}
</ref> It was discovered that Einstein's universe is unstable, and that small fluctuations cause it to collapse or turn into a de Sitter universe.

Historically, proposed solutions included the ''Phoenix universe'' of Georges Lemaître,<ref>{{Cite journal |last=Lemaître |first=Georges |title=The expanding universe |journal=Annales de la Société Scientifique de Bruxelles |volume=47A |page=49 |date=1933}}, English in ''Gen. Rel. Grav.'' '''29''':641–680, 1997.</ref> the related [[oscillatory universe]] of [[Richard Chase Tolman]],<ref>{{Cite book |author=R. C. Tolman |title= Relativity, Thermodynamics, and Cosmology |location=Oxford |publisher=Clarendon Press |date=1934 |isbn=978-0-486-65383-9 |lccn=34032023}} Reissued (1987) New York: Dover {{ISBN|0-486-65383-8}}.</ref> and the [[Mixmaster universe]] of [[Charles Misner]]. Lemaître and Tolman proposed that a universe undergoing a number of cycles of contraction and expansion could come into thermal equilibrium. Their models failed, however, because of the buildup of [[entropy]] over several cycles. Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the Universe ''more'' chaotic, could lead to statistical homogeneity and isotropy.<ref name="mtw" /><ref>{{Cite journal |title=Mixmaster universe |doi=10.1088/1751-8113/41/15/155201 |first1=Charles W. |last1=Misner |date=1969 |journal=[[Physical Review Letters]] |volume=22 |issue=15 |pages=1071–74 |last2=Leach |first2=P G L |bibcode=2008JPhA...41o5201A |s2cid=119588491 }}</ref>

In 1965, Erast Gliner proposed a unique assumption regarding the early Universe's pressure in the context of the Einstein–Friedmann equations. According to his idea, the pressure was negatively proportional to the energy density. This relationship between pressure and energy density served as the initial theoretical prediction of dark energy.{{citation needed|date=October 2024}}

In the early 1970s, [[Yakov Zeldovich]] noticed the flatness and horizon problems of Big Bang cosmology; before his work, cosmology was presumed to be symmetrical on purely philosophical grounds.<ref name="Earman-Mosterín"/> In the Soviet Union, this and other considerations led [[Vladimir Belinski]] and [[Isaak Khalatnikov]] to analyze the chaotic [[BKL singularity]] in general relativity.{{citation needed|date=October 2024}} Misner's [[Mixmaster universe]] attempted to use this chaotic behavior to solve the cosmological problems, with limited success.{{citation needed|date=October 2024}}

====False vacuum====
{{Main|False vacuum}}
In the late 1970s, [[Sidney Coleman]] applied the [[instanton]] techniques developed by [[Alexander Markovich Polyakov|Alexander Polyakov]] and collaborators to study the fate of the [[false vacuum]] in [[quantum field theory]]. Like a metastable phase in [[statistical mechanics]]—water below the freezing temperature or above the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition. Coleman found the most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume. He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology.

The universe could have been spontaneously created from nothing (no [[space]], [[time]], nor [[matter]]) by [[quantum fluctuation]]s of metastable false vacuum causing an expanding bubble of true vacuum.<ref name="url[1404.1207] Spontaneous creation of the universe from nothing">
{{cite journal
 |last1=He   |first1=Dongshan
 |last2=Gao  |first2=Dongfeng
 |last3=Cai  |first3=Qing-yu
 |year=2014
 |title=Spontaneous creation of the universe from nothing
 |journal=[[Physical Review D]]
 |volume=89  |issue=8  |article-number=083510
 |bibcode=2014PhRvD..89h3510H   |s2cid=118371273   |doi=10.1103/PhysRevD.89.083510
 |arxiv=1404.1207    <!-- |url=https://arxiv.org/abs/1404.1207 --- redundant -->
}}
</ref>

====The Causal Universe of Brout Englert and Gunzig====
<!-- {{Main|The Causal Universe of Brout Englert and Gunzig}} --> 
In 1978 and 1979, [[Robert Brout]], [[François Englert]] and Edgard Gunzig suggested that the universe could originate from a fluctuation of Minkowski space which would be followed by a period in which the geometry would resemble De Sitter space.
This initial period would then evolve into the standard expanding universe. They noted that their proposal  makes the universe causal, as there are neither particle nor event horizons in their model. 
<ref>
{{cite journal | last1=Brout | first1=R. | last2=Englert | first2=F. | last3=Gunzig | first3=E. | title=The creation of the universe as a quantum phenomenon | journal=Annals of Physics | volume=115 | issue=1 | pages=78–106 | year=1978 | doi=10.1016/0003-4916(78)90176-8 | bibcode=1978AnPhy.115...78B }}
<br/>
{{cite journal | last1=Brout | first1=R. | last2=Englert | first2=F. | last3=Gunzig | first3=E. | title=The causal universe | journal=General Relativity and Gravitation | volume=10 | pages=1–6 | year=1979 | issue=1 | doi=10.1007/BF00757018 | bibcode=1979GReGr..10....1B }}
</ref>

====Starobinsky inflation====
{{Main|Starobinsky inflation}}
In the Soviet Union, [[Alexei Starobinsky]] noted that quantum corrections to general relativity should be important for the early universe. These generically lead to curvature-squared corrections to the [[Einstein–Hilbert action]] and a form of [[f(R) gravity|{{math|''f''(''R'')}} modified gravity]]. The solution to Einstein's equations in the presence of curvature squared terms, when the curvatures are large, leads to an effective cosmological constant. Therefore, he proposed that the early universe went through an inflationary de Sitter era.<ref>
{{cite journal
 |last=Starobinsky |first=A.A.
 |date=December 1979
 |title= Spectrum of relict gravitational radiation and the early state of the universe
 |journal=[[Journal of Experimental and Theoretical Physics Letters]]
 |volume=30  |page=682
 |bibcode=1979JETPL..30..682S
}}<br/>
{{cite journal
 |author=Starobinskii, A.A.
 |date=December 1979
 |title=Spectrum of relict gravitational radiation and the early state of the universe
 |journal=[[Pisma Zh. Eksp. Teor. Fiz.]]
 |volume=30  |page= 719
 |bibcode=1979ZhPmR..30..719S
}}
</ref> This resolved the cosmology problems and led to specific predictions for the corrections to the microwave background radiation, corrections that were then calculated in detail. Starobinsky used the action 
:<math>
S=\frac{1}{2} \int d^4 x \left(R + \frac{R^2}{6M^2} \right)
</math>
which corresponds to the potential
:<math>\quad V(\phi)=\Lambda^4 \left(1 - e^{-\sqrt{2/3} \phi/M^2_p} \right)^2 </math>
in the Einstein frame. This results in the observables: <math> n_s=1 - \frac{2}{N}, \qquad r=\frac{12}{N^2}.</math><ref>
{{cite journal
 |last1=Ade |first1=P.A.R.
 |display-authors=etal
 |year=2016
 |title=Planck 2015 results. XX. Constraints on inflation
 |journal=[[Astronomy & Astrophysics]]
 |volume=594 |page=17
 |arxiv=1502.02114 |doi=10.1051/0004-6361/201525898
 |bibcode=2016A&A...594A..20P |s2cid=119284788
}}
</ref>

====Monopole problem====
In 1978, Zeldovich noted the magnetic monopole problem, which was an unambiguous quantitative version of the horizon problem, this time in a subfield of particle physics, which led to several speculative attempts to resolve it. In 1980, Alan Guth realized that false vacuum decay in the early universe would solve the problem, leading him to propose a scalar-driven inflation. Starobinsky's and Guth's scenarios both predicted an initial de Sitter phase, differing only in mechanistic details.

===Early inflationary models===
[[Image:Horizonte inflacionario.svg|thumb|upright=1.4|The physical size of the [[Hubble radius]] (solid line) as a function of the linear expansion (scale factor) of the universe. During cosmological inflation, the Hubble radius is constant. The physical wavelength of a perturbation mode (dashed line) is also shown. The plot illustrates how the perturbation mode grows larger than the horizon during cosmological inflation before coming back inside the horizon, which grows rapidly during radiation domination. If cosmological inflation had never happened, and radiation domination continued back until a [[gravitational singularity]], then the mode would never have been inside the horizon in the very early universe, and no [[causality (physics)|causal]] mechanism could have ensured that the universe was homogeneous on the scale of the perturbation mode.]]
Guth proposed inflation in January 1981 to explain the nonexistence of magnetic monopoles;<ref name=SLAC>[[Stanford Linear Accelerator Center|SLAC]] seminar, "{{10^|−35}} seconds after the Big Bang", 23 January 1980. See {{harvp|Guth|1997|p=186}}</ref><ref name="guth">
{{cite journal
 |doi=10.1103/PhysRevD.23.347
 |title=Inflationary universe: A possible solution to the horizon and flatness problems
 |url=http://www.astro.rug.nl/~weygaert/tim1publication/cosmo2007/literature/inflationary.universe.guth.physrevd-1981.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.astro.rug.nl/~weygaert/tim1publication/cosmo2007/literature/inflationary.universe.guth.physrevd-1981.pdf |archive-date=2022-10-09 |url-status=live
 |year=1981
 |last1=Guth |first1=Alan H.
 |journal=[[Physical Review D]]
 |volume=23 |issue=2 |pages=347–356
 |bibcode=1981PhRvD..23..347G |doi-access=free
}}
</ref> it was Guth who coined the term "inflation".<ref name="peebles 17">{{harvp|Peebles|1993|at=ch&nbsp;17}}</ref> At the same time, Starobinsky argued that quantum corrections to gravity would replace the supposed initial singularity of the Universe with an exponentially expanding de Sitter phase.<ref>
{{cite journal
 |first=Alexei A. |last=Starobinsky
 |year=1980
 |title=A new type of isotropic cosmological models without singularity
 |journal=[[Physics Letters B]]
 |volume=91 |issue=1 |pages=99–102
 |bibcode=1980PhLB...91...99S |doi=10.1016/0370-2693(80)90670-X
}}
</ref> In October 1980, Demosthenes Kazanas suggested that exponential expansion could eliminate the [[particle horizon]] and perhaps solve the horizon problem,<ref>
{{cite journal
 |first=Demosthenes |last=Kazanas <!-- |author-link=Demosthenes Kazanas -->
 |date=October 1980
 |title=Dynamics of the universe and spontaneous symmetry breaking
 |journal=[[Astrophysical Journal]]
 |volume=241 |pages=L59–63
 |doi=10.1086/183361 |doi-access=free
 |bibcode=1980ApJ...241L..59K
}}
</ref><ref>
{{cite conference
 |first=Demosthenes |last=Kazanas <!-- |author-link=Demosthenes Kazanas -->
 |date= 2007
 |publication-date=2009
 |title=Cosmological Inflation: A Personal Perspective
 |editor1=Contopoulos, G.
 |editor2=Patsis, P.A.
 |book-title=Chaos in Astronomy: Conference 2007
 |series=Astrophysics and Space Science Proceedings Vol. 8
 |pages=485–496
 |publisher=Springer Science & Business Media
 |isbn=978-3-540-75825-9  |s2cid=14520885
 |arxiv=0803.2080  |bibcode=2009ASSP....8..485K
 |doi=10.1007/978-3-540-75826-6_49
 |url=https://books.google.com/books?id=QfipHB0XK58C&pg=PA485
}}
</ref> while [[Katsuhiko Sato (physicist)|Katsuhiko Sato]] suggested that an exponential expansion could eliminate [[Domain wall (string theory)|domain walls]] (another kind of exotic relic).<ref>
{{Cite journal
 |first=K. |last=Sato
 |year=1981
 |title=Cosmological baryon number domain structure and the first order phase transition of a vacuum
 |journal=[[Physics Letters B]]
 |volume=33  |issue=1  |pages=66–70
 |bibcode=1981PhLB...99...66S
 |doi=10.1016/0370-2693(81)90805-4
}}
</ref> In 1981, Einhorn and Sato<ref>
{{Cite journal
 |last1=Einhorn  |first1=Martin B.
 |last2=Sato     |first2=Katsuhiko 
 |year=1981
 |title=Monopole production in the very early universe, in a first-order phase transition
 |journal=[[Nuclear Physics B]]
 |volume=180  |issue=3  |pages=385–404
 |doi=10.1016/0550-3213(81)90057-2
 |bibcode=1981NuPhB.180..385E
}}
</ref> published a model similar to Guth's and showed that it would resolve the puzzle of the [[magnetic monopole]] abundance in Grand Unified Theories. Like Guth, they concluded that such a model not only required fine tuning of the cosmological constant, but also would likely lead to a much too granular universe, i.e., to large density variations resulting from bubble wall collisions.

Guth proposed that as the early universe cooled, it was trapped in a false vacuum with a high energy density, which is much like a cosmological constant. As the very early universe cooled it was trapped in a [[metastability|metastable]] state (it was supercooled), which it could only decay out of through the process of [[nucleation|bubble nucleation]] via [[quantum tunneling]]. Bubbles of [[vacuum state|true vacuum]] spontaneously form in the sea of false vacuum and rapidly begin expanding at the [[speed of light]]. Guth recognized that this model was problematic because the model did not reheat properly: when the bubbles nucleated, they did not generate radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. In any one causal patch it is likely that only one bubble would nucleate.
{{clear}}
{{Blockquote|
... {{harvp|Kazanas|1980}} called this phase of the early Universe "de Sitter's phase". The name "inflation" was given by {{harvp|Guth|1981}}. ... Guth himself did not refer to work of Kazanas until he published a book on the subject, under the title ''The Inflationary Universe: The quest for a new theory of cosmic origin'' (1997),<ref name=guth97/> where he apologizes for not having referenced the work of Kazanas and of others, related to inflation.<ref>
{{cite book
 |last=Contopoulos |first=George
 |year=2004
 |title=Adventures in Order and Chaos: A scientific autobiography
 |volume=313 |pages=88–89
 |publisher=Springer Science & Business Media
 |isbn=978-1-4020-3040-6
 |url=https://books.google.com/books?id=3UXak_7yR3MC&pg=PA88
}}
</ref>
}}

===Slow-roll inflation===
{{Main|inflaton}}
The bubble collision problem was solved by [[Andrei Linde]]<ref name="linde">{{cite journal |last1=Linde |first1=Andrei |date=1982 |title=A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems |journal=[[Physics Letters B]] |volume=108 |issue=6 |pages=389–393 |bibcode=1982PhLB..108..389L |doi=10.1016/0370-2693(82)91219-9}}</ref> and independently by [[Andreas Albrecht (cosmologist)|Andreas Albrecht]] and [[Paul Steinhardt]]<ref name="albrecht">{{cite journal |doi=10.1103/PhysRevLett.48.1220 |title=Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking |date=1982 |last1=Albrecht |first1=Andreas |last2=Steinhardt |first2=Paul |journal=[[Physical Review Letters]] |volume=48 |issue=17 |pages=1220–1223 |bibcode=1982PhRvL..48.1220A |url=http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/07/060.pdf |archive-url=https://web.archive.org/web/20120130063002/http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/07/060.pdf |archive-date=30 January 2012  }}</ref> in a model named ''new inflation'' or ''slow-roll inflation'' (Guth's model then became known as ''old inflation'').<ref name=Smeenk-2018/>{{rp|221}} In this model, instead of tunneling out of a false vacuum state, inflation occurred by a [[scalar field]] rolling down a potential energy hill. When the field rolls very slowly compared to the expansion of the Universe, inflation occurs. However, when the hill becomes steeper, inflation ends and reheating can occur.

=== Quantum fluctuations ===
{{Main|Primordial fluctuations}}
Eventually, it was shown that new inflation does not produce a perfectly symmetric universe, but that quantum fluctuations in the inflaton are created. These fluctuations form the primordial seeds for all structure created in the later universe.<ref name=Hartle>{{cite book |last=Hartle |first=J.B. |year=2003 |title=Gravity: An introduction to Einstein's general relativity |edition=1st |publisher=Addison Wesley |isbn=978-0-8053-8662-2 |page=[https://archive.org/details/gravityintroduct00hart_100/page/n423 411] |url=https://archive.org/details/gravityintroduct00hart_100 |url-access=limited |via=archive.org }}</ref> These fluctuations were first calculated by [[Viatcheslav Mukhanov]] and G. V. Chibisov in analyzing Starobinsky's similar model.<ref>See {{harvp|Linde|1990}} and {{harvp|Mukhanov|2005}}.</ref><ref>{{Cite journal |last1=Chibisov |first1=Viatcheslav F. |last2=Chibisov |first2=G. V. |date=1981 |title=Quantum fluctuation and "nonsingular" universe |journal=[[JETP Letters]] |volume=33 |pages=532–535 |bibcode=1981JETPL..33..532M}}</ref><ref>{{cite journal |first=Viatcheslav F. |last=Mukhanov |author-link=Viatcheslav Mukhanov |date=1982 |title=The vacuum energy and large scale structure of the universe |journal=[[Soviet Physics JETP]] |volume=56 |issue=2 |pages=258–265 |bibcode=1982JETP...56..258M }}</ref> In the context of inflation, they were worked out independently of the work of Mukhanov and Chibisov at the three-week 1982 Nuffield Workshop on the Very Early Universe at [[University of Cambridge|Cambridge University]].<ref>See {{harvp|Guth|1997}} for a popular description of the workshop, or ''The Very Early Universe'', eds Gibbon, Hawking, & Siklos, {{ISBN|0-521-31677-4}}, for a more detailed report.</ref> The fluctuations were calculated by four groups working separately over the course of the workshop: [[Stephen Hawking]];<ref>{{cite journal |last=Hawking |first=S.W. |author-link=Stephen Hawking |year=1982 |title=The development of irregularities in a single bubble inflationary universe |journal=[[Physics Letters B]] |volume=115 |issue=4 |pages=295–297 |bibcode=1982PhLB..115..295H |doi=10.1016/0370-2693(82)90373-2}}</ref> Starobinsky;<ref>{{cite journal|last=Starobinsky |first=Alexei A. |year=1982 |title=Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations|journal=[[Physics Letters B]] |volume=117 |issue=3–4 |pages=175–178 |bibcode=1982PhLB..117..175S |doi=10.1016/0370-2693(82)90541-X }}</ref> [[Alan Guth]] and [[So-Young Pi]];<ref>{{cite journal |last1=Guth |first1=Alan H. |author1-link=Alan Guth |first2=So-Young |last2=Pi |author2-link=So-Young Pi |year=1982 |title=Fluctuations in the new inflationary universe |journal=[[Physical Review Letters]] |volume=49 |issue=15 |pages=1110–1113 |bibcode=1982PhRvL..49.1110G |doi=10.1103/PhysRevLett.49.1110}}</ref> and [[James M. Bardeen|James Bardeen]], [[Paul Steinhardt]] and [[Michael Turner (cosmologist)|Michael Turner]].<ref>{{cite journal |last1=Bardeen |first1=James M. |author1-link=James M. Bardeen |last2=Steinhardt |first2=Paul J. |author2-link=Paul Steinhardt |last3=Turner |first3=Michael S. |author3-link=Michael Turner (cosmologist) |year=1983 |title=Spontaneous creation of almost scale-free density perturbations in an inflationary universe |journal=[[Physical Review D]] |volume=28 |issue= 4|pages=679–693 |bibcode=1983PhRvD..28..679B |doi=10.1103/PhysRevD.28.679 }}</ref>

=== Demise of topological defects rival ===
Once it became clear that the CMB would be a key experimental testing ground for cosmological models, possible tests for alternative approaches to inflation began to be considered. One rival theory that dates from the same time at Guth's work was the concept of cosmological [[Topological_defect#Cosmological_defects|topological defects]].
The idea was that as the very early universe cools from an initial hot, dense state it triggered a series of [[phase transition]]s much like what happens in condensed-matter systems  such as [[vortices]] in [[liquid helium]]. Topological defects in cosmology are consequences degenerate vacuum states of the universe, called the [[vacuum manifold]], after a symmetry-breaking phase transition. [[Magnetic monopoles]] were one example of a stable topological defect predicted by [[grand unified theories]] of the early [[universe]]. Development of these models throughout the 1980s and 1990s eventually resulted in predictions which could be tested by sensitive measurement of the CMB.<ref>{{Cite journal |last1=Albrecht |first1=Andreas |last2=Coulson |first2=David |last3=Ferreira |first3=Pedro |last4=Magueijo |first4=Joao |date=1996-02-26 |title=Causality, Randomness, and the Microwave Background |url=https://link.aps.org/doi/10.1103/PhysRevLett.76.1413 |journal=Physical Review Letters |language=en |volume=76 |issue=9 |pages=1413–1416 |doi=10.1103/PhysRevLett.76.1413 |pmid=10061717 |issn=0031-9007|arxiv=astro-ph/9505030 |bibcode=1996PhRvL..76.1413A }}</ref> Detailed measurements by the [[Wilkinson Microwave Anisotropy Probe]] provide strong evidence in favor of cosmic inflation instead.<ref>{{Cite journal |last1=Dodelson |first1=Scott |last2=Knox |first2=Lloyd |date=2000-04-17 |title=Dark Energy and the Cosmic Microwave Background Radiation |url=https://link.aps.org/doi/10.1103/PhysRevLett.84.3523 |journal=Physical Review Letters |volume=84 |issue=16 |pages=3523–3526 |doi=10.1103/PhysRevLett.84.3523|pmid=11019136 |arxiv=astro-ph/9909454 |bibcode=2000PhRvL..84.3523D }}</ref> (Models which combine these concepts remain viable).<ref name=Smeenk-2018/>{{rp|231}}<ref>{{Cite journal |last=Turner |first=Michael S. |date=2022-09-26 |title=The Road to Precision Cosmology |url=https://www.annualreviews.org/doi/10.1146/annurev-nucl-111119-041046 |journal=Annual Review of Nuclear and Particle Science |language=en |volume=72 |issue=1 |pages=1–35 |doi=10.1146/annurev-nucl-111119-041046 |issn=0163-8998|arxiv=2201.04741 |bibcode=2022ARNPS..72....1T }}</ref>

==Observational status==
Inflation is a mechanism for realizing the [[cosmological principle]], which is the basis of the standard model of physical cosmology: it accounts for the homogeneity and isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the [[cosmic microwave background]] made by the [[Planck (spacecraft)|Planck spacecraft]].<ref name="Ade-2016">{{Cite journal |collaboration=Planck Collaboration |last1=Ade |first1=P.A.R. |display-authors=etal |date=2016-10-01 |title=Planck 2015 results. XIII. Cosmological parameters |journal=Astronomy & Astrophysics |volume=594 |pages=A13 |doi=10.1051/0004-6361/201525830 |issn=0004-6361 |bibcode=2016A&A...594A..13P |arxiv=1502.01589|s2cid=119262962 }}</ref> This analysis shows that the Universe is flat to within {{sfrac| 1 |2}} percent, and that it is homogeneous and isotropic to one part in 100,000.

Inflation predicts that the structures visible in the Universe today formed through the [[gravitational collapse]] of perturbations that were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations, called a [[Scale invariance#Cosmology|nearly-scale-invariant]] [[Gaussian random field]] is very specific and has only two free parameters. One is the amplitude of the spectrum and the ''[[spectral index]]'', which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealized [[de Sitter universe]]).{{efn|
Perturbations can be represented by [[Fourier modes]] of a [[wavelength]]. Each Fourier mode is [[Normal distribution|normally distributed]] (usually called Gaussian) with mean zero. Different Fourier components are uncorrelated. The variance of a mode depends only on its wavelength in such a way that within any given volume each wavelength contributes an equal amount of [[Spectral density|power]] to the spectrum of perturbations. Since the Fourier transform is in three dimensions, this means that the variance of a mode goes as 1/{{mvar|k}}{{sup|3}} to compensate for the fact that within any volume, the number of modes with a given wavenumber {{mvar|k}} goes as {{mvar|k}}{{sup|3}}.
}}
The other free parameter is the tensor to scalar ratio. The simplest inflation models, those without [[Fine-tuned universe|fine-tuning]], predict a [[Tensor field|tensor]] to scalar ratio near 0.1&nbsp;.<ref name="boyle2">{{cite journal |last1=Boyle |first1=Latham A. |last2=Steinhardt |first2=Paul J. |author2-link=Paul Steinhardt |last3=Turok |first3=Neil |author3-link=Neil Turok |date=2006-03-24 |title=Inflationary Predictions for Scalar and Tensor Fluctuations Reconsidered |journal=[[Physical Review Letters]] |volume=96 |issue=11 |article-number=111301 |arxiv=astro-ph/0507455 |bibcode=2006PhRvL..96k1301B |doi=10.1103/PhysRevLett.96.111301 |pmid=16605810 |s2cid=10424288}}</ref>

Inflation predicts that the observed perturbations should be in [[thermal equilibrium]] with each other (these are called ''[[adiabatic]]'' or ''[[Isentropic process|isentropic]]'' perturbations). This structure for the perturbations has been confirmed by the [[Planck (spacecraft)|Planck spacecraft]], [[Wilkinson Microwave Anisotropy Probe|WMAP]] spacecraft and other cosmic microwave background (CMB) experiments, and [[galaxy survey]]s, especially the ongoing [[Sloan Digital Sky Survey]].<ref name=sdss2>{{cite journal |last1=Tegmark |first1=Max |display-authors=etal |date=August 2006 |title=Cosmological constraints from the SDSS luminous red galaxies |journal=[[Physical Review D]] |volume=74 |issue=12 |article-number=123507 |arxiv=astro-ph/0608632 |bibcode=2006PhRvD..74l3507T |doi=10.1103/PhysRevD.74.123507 |s2cid=1368964 |hdl=1811/48518}}</ref> These experiments have shown that the one part in 100,000&nbsp;inhomogeneities observed have exactly the form predicted by theory. There is evidence for a slight deviation from scale invariance. The ''[[spectral index]]'', {{mvar|n}}{{sub|s}} is one for a scale-invariant Harrison–Zel'dovich spectrum. The simplest inflation models predict that {{mvar|n}}{{sub|s}} is between 0.92 and 0.98&nbsp;.<ref name=myths2>{{cite journal |last=Steinhardt |first=Paul J. |author2-link=Paul Steinhardt |date=2004 |title=Cosmological perturbations: Myths and facts |journal=[[Modern Physics Letters A]] |volume=19 |issue=13 & 16 |pages=967–982 |bibcode=2004MPLA...19..967S |doi=10.1142/S0217732304014252 |s2cid=42066874}}</ref><ref name="boyle2"/><ref name=tegmark2>{{cite journal |last=Tegmark |first=Max |date=2005 |title=What does inflation really predict?|journal=[[Journal of Cosmology and Astroparticle Physics]] |volume=2005 |issue=4 |page=001 |arxiv=astro-ph/0410281 |bibcode=2005JCAP...04..001T |doi=10.1088/1475-7516/2005/04/001 |s2cid=17250080 }}</ref>{{efn|
This is known as a "red" spectrum, in analogy to [[redshift]], because the spectrum has more power at longer wavelengths.
}} This is the range that is possible without [[Fine-tuned universe|fine-tuning]] of the parameters related to energy.<ref name=tegmark2/> From Planck data it can be inferred that {{mvar|n}}{{sub|s}}=0.968 ± 0.006,<ref name="Ade-2016"/><ref>{{cite journal |last1=Ade |first1=P.A.R. |collaboration=Planck Collaboration |date=October 2016 |title=Planck 2015 results. XX.&nbsp;Constraints on inflation |journal=[[Astronomy & Astrophysics]] |volume=594 |page=A20 |doi=10.1051/0004-6361/201525898 |issn=0004-6361 |bibcode=2016A&A...594A..20P |arxiv=1502.02114|s2cid=119284788 }}</ref> and a [[Tensor field|tensor]] to scalar ratio that is less than 0.11&nbsp;. These are considered an important confirmation of the theory of inflation.<ref name="wmap2"/>

Various inflation theories have been proposed that make radically different predictions, but they generally have much more [[Fine-tuning (physics)|fine-tuning]] than should be necessary.<ref name=myths2/><ref name=boyle2/> As a physical model, however, inflation is most valuable in that it robustly predicts the initial conditions of the Universe based on only two adjustable parameters: the spectral index (that can only change in a small range) and the amplitude of the perturbations. Except in contrived models, this is true regardless of how inflation is realized in particle physics.

Occasionally, effects are observed that appear to contradict the simplest models of inflation. The first-year [[Wilkinson Microwave Anisotropy Probe|WMAP]] data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature.<ref>{{cite journal|last1=Spergel |first1=D.N. |display-authors=etal |date=2003 |title=First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters |journal=[[Astrophysical Journal Supplement Series]] |volume=148 |issue=1 |pages=175–194 |arxiv=astro-ph/0302209 |bibcode=2003ApJS..148..175S |doi=10.1086/377226 |s2cid=10794058 }}</ref> However, the third-year data revealed that the effect was a statistical anomaly.<ref name=wmap2/> Another effect remarked upon since the first cosmic microwave background satellite, the [[Cosmic Background Explorer]] is that the amplitude of the [[quadrupole moment]] of the CMB is unexpectedly low and the other low multipoles appear to be preferentially aligned with the [[plane of the ecliptic|ecliptic plane]]. Some have claimed that this is a signature of [[non-Gaussianity]] and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to quantum corrections or new physics, foreground contamination, or even [[publication bias]].<ref>See [[Cosmic microwave background#Anomalies]] for details and references.</ref>

[[File:History of the Universe.svg|thumb|upright=2.3| [[Primordial gravitational wave]]s, hypothesized to arise from cosmic inflation, would alter the polarization of the [[cosmic background radiation]].<ref name="NASA-20140317">{{cite web |last=Clavin |first=Whitney |title=NASA Technology Views Birth of the Universe |url=https://www.jpl.nasa.gov/news/nasa-technology-views-birth-of-the-universe/ |date=17 March 2014 |work=[[NASA]] |access-date=17 March 2014 }}</ref><ref name="NYT-20140317">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Space Ripples Reveal Big Bang's Smoking Gun |url=https://www.nytimes.com/2014/03/18/science/space/detection-of-waves-in-space-buttresses-landmark-theory-of-big-bang.html |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2014/03/18/science/space/detection-of-waves-in-space-buttresses-landmark-theory-of-big-bang.html |archive-date=2022-01-01 |url-access=limited |date=17 March 2014 |work=[[The New York Times]]|access-date=17 March 2014 }}{{cbignore}}</ref>]]
An experimental program is underway to further test inflation with more precise CMB measurements. In particular, high precision measurements of the so-called "B-modes" of the [[Cosmic microwave background radiation#Polarization|polarization]] of the background radiation could provide evidence of the [[gravitational radiation]] produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models ({{10^|15}}~{{10^|16}} [[GeV]]) is correct.<ref name=boyle2/><ref name=tegmark2/> In March 2014, the [[BICEP2]] team announced B-mode CMB polarization confirming inflation had been demonstrated. The team announced the tensor-to-scalar power ratio {{mvar|r}} was between 0.15 and 0.27 (rejecting the [[null hypothesis]]; {{mvar|r}} is expected to be 0 in the absence of inflation).<ref name="five years">{{cite journal |last1=Grant |first1=Andrew |title=Five years after BICEP2 |journal=[[Physics Today]] |date=2019 |issue=3 |article-number=30948 |doi=10.1063/PT.6.3.20190326a |bibcode=2019PhT..2019c0948G |s2cid=241938983 }}</ref> However, on 19 June 2014, lowered confidence in confirming the findings was reported;<ref name=PRL-20140619>{{cite journal |last1=Ade |first1=P.A.R. |collaboration=BICEP2 Collaboration |title=Detection of B-mode polarization at degree angular scales by BICEP2 |date=19 June 2014 |journal=[[Physical Review Letters]] |volume=112 |issue=24 |article-number=241101 |doi=10.1103/PhysRevLett.112.241101 |arxiv=1403.3985 |bibcode=2014PhRvL.112x1101B |display-authors=etal |pmid=24996078|s2cid=22780831 }}</ref><ref name=NYT-20140619>{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=19 June 2014 |title=Astronomers hedge on Big Bang detection claim |newspaper=[[The New York Times]] |url=https://www.nytimes.com/2014/06/20/science/space/scientists-debate-gravity-wave-detection-claim.html |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2014/06/20/science/space/scientists-debate-gravity-wave-detection-claim.html |archive-date=2022-01-01 |url-access=limited |access-date=20 June 2014 }}{{cbignore}}</ref><ref name="BBC-20140619">{{cite news |last=Amos |first=Jonathan |date=19 June 2014 |title=Cosmic inflation: Confidence lowered for Big Bang signal |series=[[BBC News]] |url=https://www.bbc.com/news/science-environment-27935479 |access-date=20 June 2014 }}</ref> on 19 September 2014, a further reduction in confidence was reported<ref name=AXV-20140919>{{cite journal |last1=Ade |first1=P.A.R. |collaboration=Planck Collaboration Team |year=2016 |title=Planck intermediate results. XXX.&nbsp;The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes |journal=Astronomy & Astrophysics |volume=586 |issue=133 |page=A133 |arxiv=1409.5738 |doi=10.1051/0004-6361/201425034 |bibcode=2016A&A...586A.133P |s2cid=9857299 }}</ref><ref name=NYT-20140922>{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=22 September 2014 |title=Study confirms criticism of Big Bang finding |newspaper=[[The New York Times]] |url=https://www.nytimes.com/2014/09/23/science/space/study-confirms-criticism-of-big-bang-finding.html |url-access=limited |access-date=22 September 2014 |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2014/09/23/science/space/study-confirms-criticism-of-big-bang-finding.html |archive-date=2022-01-01 }}{{cbignore}}</ref> and, on 30 January 2015, even less confidence yet was reported.<ref name="NASA-20150130">{{cite press release |last=Clavin |first=Whitney |date=30 January 2015 |title=Gravitational waves from early universe remain elusive |publisher=[[NASA]] |url=http://www.jpl.nasa.gov/news/news.php?release=2015-46 |access-date=30 January 2015 }}</ref><ref name=NYT-20150130>{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=30 January 2015 |title=Speck of interstellar dust obscures glimpse of Big Bang |newspaper=[[The New York Times]] |url=https://www.nytimes.com/2015/01/31/us/a-speck-of-interstellar-dust-rebuts-a-big-bang-theory.html |url-access=limited |access-date=31 January 2015 |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2015/01/31/us/a-speck-of-interstellar-dust-rebuts-a-big-bang-theory.html |archive-date=2022-01-01 }}{{cbignore}}</ref> By 2018, additional data suggested, with 95% confidence, that <math>r</math> is 0.06 or lower: Consistent with the null hypothesis, but still also consistent with many remaining models of inflation.<ref name="five years"/>

Other potentially corroborating measurements are expected from the [[Planck (spacecraft)|Planck spacecraft]], although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere.<ref>
{{cite conference
 |first1=C. |last1=Rosset
 |collaboration=PLANCK-HFI collaboration
 |year=2005
 |title=Systematic effects in CMB polarization measurements
 |book-title=Exploring the Universe: Contents and structures of the universe
 |conference=XXXIXth Rencontres de Moriond
 |arxiv=astro-ph/0502188
}}
</ref>
Other forthcoming measurements, such as those of [[21 centimeter radiation]] (radiation emitted and absorbed from neutral hydrogen before the [[population III star|first stars]] formed), may measure the power spectrum with even greater resolution than the CMB and galaxy surveys, although it is not known if these measurements will be possible or if interference with [[radio frequency|radio sources]] on Earth and in the galaxy will be too great.<ref>
{{cite journal
 |first1=A. |last1=Loeb
 |first2=M. |last2=Zaldarriaga
 |year=2004
 |title=Measuring the small-scale power spectrum of cosmic density fluctuations through 21&nbsp;cm tomography prior to the epoch of structure formation
 |journal=[[Physical Review Letters]]
 |volume=92  |issue=21  |article-number=211301
 |arxiv=astro-ph/0312134  |s2cid=30510359
 |bibcode=2004PhRvL..92u1301L  |pmid=15245272
 |doi=10.1103/PhysRevLett.92.211301
 |url=https://cds.cern.ch/record/690135
 |via=[[CERN]]
}}
</ref>

==Theoretical status==
{{unsolved|physics|Is the theory of cosmological inflation correct, and if so, what are the details of this epoch? What is the hypothetical inflaton field giving rise to inflation?}}
In Guth's early proposal, it was thought that the [[inflaton]] was the [[Higgs field]], the field that explains the mass of the elementary particles.<ref name=guth/> It is now believed by some that the inflaton cannot be the Higgs field.<ref name=guth97>
{{cite book
 |last=Guth |first=Alan |author-link=Alan Guth
 |year=1997b
 |title=The Inflationary Universe: The quest for a new theory of cosmic origin
 |publisher=[[Addison–Wesley]]
 |isbn=978-0-201-14942-5
 |url=https://archive.org/details/inflationaryuniv0000guth
 |url-access=registration |via=archive.org
}}
</ref> One problem of this identification is the current tension with experimental data at the [[Electroweak interaction|electroweak]] scale,.<ref>
{{cite journal
 |last=Salvio |first=Alberto
 |year=2013
 |title=Higgs inflation at NNLO after the boson discovery
 |journal=[[Physics Letters B]] |volume=727 |issue=1–3 |pages=234–239
 |arxiv=1308.2244 |bibcode=2013PhLB..727..234S |doi=10.1016/j.physletb.2013.10.042 |s2cid=56544999}}
</ref> Other models of inflation relied on the properties of [[Grand Unified Theory|Grand Unified Theories]].<ref name=albrecht/>

===Fine-tuning problem===
One of the most severe challenges for inflation arises from the need for [[Fine-tuning (physics)|fine tuning]]. In new inflation, the ''slow-roll conditions'' must be satisfied for inflation to occur. The slow-roll conditions say that the inflaton [[scalar potential|potential]] must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass.{{Clarify |reason=the inflaton particle has not been defined. From the note, it seems that the second condition should be that the inflaton potential should be large |date=June 2014}}{{efn|
Technically, these conditions are that the [[logarithmic derivative]] of the potential, <math>\ \epsilon = \tfrac{1}{2} \left(\tfrac{ V' }{ V }\right)^2\ </math> and second derivative <math>\ \eta = \tfrac{ V''}{ V }\ </math> are both small, where <math>\ V\ </math> is the potential, and the equations are written in [[reduced Planck units]].<ref>{{harvp|Liddle |Lyth|2000|pp=42–43}}</ref>
}}
New inflation requires the Universe to have a scalar field with an especially flat potential and special initial conditions. However, explanations for these fine-tunings have been proposed. For example, classically scale invariant field theories, where scale invariance is broken by quantum effects, provide an explanation of the flatness of inflationary potentials, as long as the theory can be studied through [[perturbation theory]].<ref>
{{cite journal
 |last1=Salvio  |first1=Alberto
 |last2=Strumia |first2=Alessandro |author-link2=Alessandro Strumia
 |date=17 March 2014
 |title=Agravity
 |journal=[[Journal of High Energy Physics]]
 |volume=2014 |issue=6 |page=80
 |arxiv=1403.4226 |bibcode=2014JHEP...06..080S
 |doi=10.1007/JHEP06(2014)080 |s2cid=256010671
}}
</ref>

Linde proposed a theory known as ''[[Chaotic inflation theory|chaotic inflation]]'' in which he suggested that the conditions for inflation were actually satisfied quite generically. Inflation will occur in virtually [[Multiverse|any universe]] that begins in a chaotic, high energy state that has a scalar field with unbounded potential energy.<ref name=chaotic>
{{cite journal
 |last=Linde |first=Andrei D.
 |date=1983
 |title=Chaotic inflation
 |journal=[[Physics Letters B]]
 |volume=129 |issue=3 |pages=171–81
 |bibcode=1983PhLB..129..177L
 |doi=10.1016/0370-2693(83)90837-7
}}
</ref>
However, in his model, the inflaton field necessarily takes values larger than one [[Planck unit]]: For this reason, these are often called ''large field'' models and the competing new inflation models are called ''small field'' models. In this situation, the predictions of [[effective field theory]] are thought to be invalid, as [[renormalization]] should cause large corrections that could prevent inflation.{{efn|
Technically, this is because the inflaton potential is expressed as a Taylor series in <math>\ \tfrac{ \mathrm{\phi} }{ m_\mathsf{Plk} }\ ,</math> where <math>\ \mathrm{\phi}\ </math> is the inflaton and <math>\ m_\mathsf{Plk}\ </math> is the [[Planck mass]]. While for a single term, such as the mass term <math>\ m^4_\mathrm{\phi} \left( \tfrac{ \mathrm{\phi} }{ m_\mathsf{Plk} }\right)^2\ ,</math> the slow roll conditions can be satisfied for <math>\ \mathrm \phi\ </math> much greater than <math>\ m_\mathsf{Plk}\ ,</math> this is precisely the situation in effective field theory in which higher order terms would be expected to contribute and destroy the conditions for inflation. The absence of these higher order corrections can be seen as another sort of fine tuning.<ref>
{{cite journal
 |last1=Alabidi |first1=Laila
 |last2=Lyth    |first2=David H.
 |year=2006
 |title=Inflation models and observation
 |journal=[[Journal of Cosmology and Astroparticle Physics]]
 |volume=2006  |issue=5  |page=016
 |arxiv=astro-ph/0510441  |bibcode=2006JCAP...05..016A
 |doi=10.1088/1475-7516/2006/05/016  |s2cid=119373837
}}
</ref>
}}
This problem has not yet been resolved and some cosmologists argue that the small field models, in which inflation can occur at a much lower energy scale, are better models.<ref>
{{cite journal
 |last=Lyth |first=David H.
 |year=1997
 |title=What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?
 |journal=[[Physical Review Letters]]
 |volume=78 |issue=10 |pages=1861–1863
 |arxiv=hep-ph/9606387 |bibcode=1997PhRvL..78.1861L
 |s2cid=119470003 |doi=10.1103/PhysRevLett.78.1861
 |url=http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+EPRINT+HEP-PH/9606387
 |archive-url=https://archive.today/20120629010941/http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+EPRINT+HEP-PH/9606387
 |archive-date=2012-06-29
}}
</ref>
While inflation depends on quantum field theory (and the [[semiclassical gravity|semiclassical approximation]] to [[quantum gravity]]) in an important way, it has not been completely reconciled with these theories.

[[Robert Brandenberger|Brandenberger]] commented on fine-tuning in another situation.<ref>
{{cite conference
 |first=Robert H. |last=Brandenberger  |author-link=Robert Brandenberger
 |date=November 2004
 |title=Challenges for inflationary cosmology
 |conference=10th International Symposium on Particles, Strings, and Cosmology
 |arxiv=astro-ph/0411671
}}
</ref>
The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. This scale is suggested to be around {{10^|16}} [[GeV]] or {{10^|−3}} times the [[Planck energy]]. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a [[hierarchy problem]]): The energy density given by the scalar potential is down by {{10^|−12}} compared to the [[Planck density]]. This is not usually considered to be a critical problem, however, because the scale of inflation corresponds naturally to the scale of gauge unification.

===Eternal inflation===
{{Main|Eternal inflation}}

In many models, the inflationary phase of the Universe's expansion lasts forever in at least some regions of the Universe. This occurs because inflating regions expand very rapidly, reproducing themselves. Unless the rate of decay to the non-inflating phase is sufficiently fast, new inflating regions are produced more rapidly than non-inflating regions. In such models, most of the volume of the Universe is continuously inflating at any given time.

All models of eternal inflation produce an infinite, hypothetical multiverse, typically a fractal. The multiverse theory has created significant dissension in the scientific community about the viability of the inflationary model.

[[Paul Steinhardt]], one of the original architects of the inflationary model, introduced the first example of eternal inflation in 1983.<ref name="steinhardt" >{{cite book |editor1-last=Gibbons |editor1-first= Gary W. |editor1-link= Gary Gibbons |editor2-first=Stephen W. |editor2-last=Hawking |editor3-last=Siklos |editor3-first= S.T.C. |title="Natural Inflation," in The Very Early Universe |publisher=Cambridge University Press |pages= 251–66 |year=1983 |isbn=978-0-521-31677-4}}</ref> He showed that the inflation could proceed forever by producing bubbles of non-inflating space filled with hot matter and radiation surrounded by empty space that continues to inflate. The bubbles could not grow fast enough to keep up with the inflation. Later that same year, [[Alexander Vilenkin]] showed that eternal inflation is generic.<ref name="vilenkin">{{cite journal|last1=Vilenkin|first1=Alexander|year=1983|title=Birth of Inflationary Universes|journal=[[Physical Review D]]|volume=27|issue=12|pages=2848–2855|bibcode=1983PhRvD..27.2848V|doi=10.1103/PhysRevD.27.2848}}</ref>

Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes lift it to previous levels. These regions in which the inflaton fluctuates upwards, expand much faster than regions in which the inflaton has a lower potential energy, and tend to dominate in terms of physical volume. It has been shown that any inflationary theory with an unbounded potential is eternal. There are well-known theorems that this steady state cannot continue forever into the past. Inflationary spacetime, which is similar to de Sitter space, is incomplete without a contracting region. However, unlike de Sitter space, fluctuations in a contracting inflationary space collapse to form a gravitational singularity, a point where densities become infinite. Therefore, it is necessary to have a theory for the Universe's initial conditions.

In eternal inflation, regions with inflation have an exponentially growing volume, while regions that are not inflating do not. This suggests that the volume of the inflating part of the Universe in the global picture is always unimaginably larger than the part that has stopped inflating, even though inflation eventually ends as seen by any single pre-inflationary observer. Scientists disagree about how to assign a probability distribution to this hypothetical anthropic landscape. If the probability of different regions is counted by volume, one should expect that inflation will never end or applying boundary conditions that a local observer exists to observe it, that inflation will end as late as possible.

Some physicists believe this paradox can be resolved by weighting observers by their pre-inflationary volume. Others believe that there is no resolution to the paradox and that the [[multiverse]] is a critical flaw in the inflationary paradigm. Paul Steinhardt, who first introduced the eternal inflationary model,<ref name="steinhardt"/> later became one of its most vocal critics for this reason.<ref name="Inflation Debate">
{{cite magazine
 |author=Steinhardt, Paul J.
 |date=April 2011
 |title=Inflation Debate: Is the theory at the heart of modern cosmology deeply flawed?
 |url=http://www.physics.princeton.edu/~steinh/0411036.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.physics.princeton.edu/~steinh/0411036.pdf |archive-date=2022-10-09 |url-status=live
 |magazine=[[Scientific American]]
 |volume=304 |issue=4 |pages=36–43
 |bibcode=2011SciAm.304d..36S
 |doi=10.1038/scientificamerican0411-36 |pmid=21495480
}}
</ref><ref>{{cite book |last=Steinhardt |first=Paul J. |chapter-url=http://www.physics.princeton.edu/~steinh/vaasrev.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.physics.princeton.edu/~steinh/vaasrev.pdf |archive-date=2022-10-09 |url-status=live |editor-last=Vaas |editor-first=Rudy |publisher=Springer |date=2011 |chapter=The Cyclic Theory of the Universe |title=Beyond the Big Bang: Competing Scenarios For An Eternal Universe |series=The Frontiers Collectuion |type=Unpublished manuscript}}{{Better source needed|reason=Was this book ever published? Can we find something else which was?|date=April 2022}}
</ref><ref>{{cite journal |last1=Ijjas |first1=Anna |last2=Steinhardt |first2=Paul J. |last3=Loeb |first3=Abraham |title=Pop Goes the Universe |journal=Scientific American |date=17 January 2017 |volume=316 |issue=2 |pages=32–39 |doi=10.1038/scientificamerican0217-32 |jstor=26047449 |pmid=28118351 |bibcode=2017SciAm.316b..32I |url=https://www.cfa.harvard.edu/~loeb/sciam3.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.cfa.harvard.edu/~loeb/sciam3.pdf |archive-date=2022-10-09 |url-status=live}}</ref>

===Initial conditions===
Some physicists have tried to avoid the initial conditions problem by proposing models for an eternally inflating universe with no origin.<ref>{{Cite journal|last1=Carroll|first1=Sean M.|last2=Chen|first2=Jennifer|date=2005|title=Does inflation provide natural initial conditions for the universe?|journal=[[General Relativity and Gravitation]]|volume=37|issue=10|pages=1671–4|arxiv=gr-qc/0505037|bibcode=2005GReGr..37.1671C|doi=10.1007/s10714-005-0148-2|s2cid=120566514}}</ref><ref>{{cite journal|last1=Aguirre|first1=Anthony|last2=Gratton|first2=Steven|date=2003|title=Inflation without a beginning: A null boundary proposal|journal=[[Physical Review D]]|volume=67|issue=8|article-number=083515|arxiv=gr-qc/0301042|bibcode=2003PhRvD..67h3515A|doi=10.1103/PhysRevD.67.083515|s2cid=37260723}}</ref><ref>{{cite journal|last1=Aguirre|first1=Anthony|last2=Gratton|first2=Steven|date=2002|title=Steady-State Eternal Inflation|url=https://cds.cern.ch/record/526126|journal=[[Physical Review D]]|volume=65|issue=8|article-number=083507|arxiv=astro-ph/0111191|bibcode=2002PhRvD..65h3507A|doi=10.1103/PhysRevD.65.083507|s2cid=118974302}}</ref> These models propose that while the Universe, on the largest scales, expands exponentially it was, is and always will be, spatially infinite and has existed, and will exist, forever.

Other proposals attempt to describe the ex nihilo creation of the Universe based on [[quantum cosmology]] and the following inflation. Vilenkin put forth one such scenario.<ref name="vilenkin" /> [[Hartle–Hawking state|Hartle and Hawking]] offered the [[no-boundary proposal]] for the initial creation of the Universe in which inflation comes about naturally.<ref>{{cite journal|last1=Hartle|first1=J.|last2=Hawking|first2=S.|date=1983|title=Wave function of the universe|journal=[[Physical Review D]]|volume=28|issue=12|pages=2960–2975|bibcode=1983PhRvD..28.2960H|doi=10.1103/PhysRevD.28.2960|s2cid=121947045 }}; See also Hawking (1998).</ref><ref name="PHYS-20180502">{{cite web |author=Staff ([[University of Cambridge]]) |title=Taming the multiverse—Stephen Hawking's final theory about the big bang |url=https://phys.org/news/2018-05-multiversestephen-hawking-theory-big.html |date=2 May 2018 |work=[[Phys.org]] |access-date=2 May 2018 }}</ref><ref name="JHEP-20180420">{{cite journal |last1=Hawking |first1=Stephen |last2=Hertog |first2=Thomas |author-link1=Stephen Hawking |author-link2=Thomas Hertog |title=A smooth exit from eternal inflation? |arxiv=1707.07702 |date=20 April 2018 |journal=[[Journal of High Energy Physics]] |volume=2018 |issue=4 |page=147 |doi=10.1007/JHEP04(2018)147|bibcode=2018JHEP...04..147H |s2cid=13745992 }}</ref>

Guth described the inflationary universe as the "ultimate free lunch":<ref>Hawking (1998), p. 129.</ref><ref>[[wikiquote:Alan Guth|Wikiquote]].</ref> new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) the [[first law of thermodynamics]] ([[energy conservation]]) and the [[second law of thermodynamics]] ([[entropy]] and the [[arrow of time]] problem). However, while there is consensus that this solves the initial conditions problem, some have disputed this, as it is much more likely that the Universe came about by a [[quantum fluctuation]]. [[Don Page (physicist)|Don Page]] was an outspoken critic of inflation because of this anomaly.<ref>{{cite journal|last1=Page|first1=Don N.|date=1983|title=Inflation does not explain time asymmetry|journal=[[Nature (journal)|Nature]]|volume=304|issue=5921|pages=39–41|bibcode=1983Natur.304...39P|doi=10.1038/304039a0|s2cid=4315730}}; see also [[Roger Penrose]]'s book [[The Road to Reality: A Complete Guide to the Laws of the Universe]].</ref> He stressed that the thermodynamic [[arrow of time]] necessitates low [[entropy]] initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase.

Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle–Hawking initial state.<ref>{{Cite journal |last1=Hawking |first1=Stephen W. |last2=Page |first2=Don N. |date=1988 |title=How probable is inflation? |journal=[[Nuclear Physics B]] |volume=298 |issue=4 |pages=789–809 |bibcode=1988NuPhB.298..789H |doi=10.1016/0550-3213(88)90008-9}}</ref> Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the Universe.<ref name=Steinhardt2011/><ref name="SteinhardtTurok2007"/>{{rp |223–225}} However, Albrecht and Lorenzo Sorbo argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state is much higher than that of a non-inflationary cosmos. This is because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than that for a non-inflationary alternative, which outweighs any entropic considerations.<ref>{{Cite journal|last1=Albrecht|first1=Andreas|last2=Sorbo|first2=Lorenzo|date=2004|title=Can the universe afford inflation?|journal=[[Physical Review D]]|volume=70|issue=6|article-number=063528|arxiv=hep-th/0405270|bibcode=2004PhRvD..70f3528A|doi=10.1103/PhysRevD.70.063528|s2cid=119465499}}</ref>

Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects.<ref>{{Cite journal|last1=Martin|first1=Jerome|last2=Brandenberger|first2=Robert|date=2001|title=The trans-Planckian problem of inflationary cosmology|journal=[[Physical Review D]]|volume=63|issue=12|article-number=123501|arxiv=hep-th/0005209|bibcode=2001PhRvD..63l3501M|doi=10.1103/PhysRevD.63.123501|s2cid=119329384}}</ref> Since the energy scale of inflation and the Planck scale are relatively close, some of the quantum fluctuations that have made up the structure in our universe were smaller than the Planck length before inflation. Therefore, there ought to be corrections from Planck-scale physics, in particular the unknown quantum theory of gravity. Some disagreement remains about the magnitude of this effect: about whether it is just on the threshold of detectability or completely undetectable.<ref>{{Cite journal|last1=Martin|first1=Jerome|last2=Ringeval|first2=Christophe|date=2004|title=Superimposed Oscillations in the WMAP Data?|journal=[[Physical Review D]]|volume=69|issue=8|article-number=083515|arxiv=astro-ph/0310382|bibcode=2004PhRvD..69h3515M|doi=10.1103/PhysRevD.69.083515|s2cid=118889842}}</ref>

===Hybrid inflation===
Another kind of inflation, called ''hybrid inflation'', is an extension of new inflation. It introduces additional scalar fields, so that while one of the scalar fields is responsible for normal slow roll inflation, another triggers the end of inflation: when inflation has continued for sufficiently long, it becomes favorable to the second field to decay into a much lower energy state.<ref>{{Cite conference|last1= Brandenberger|first1= Robert H.|title= A Status Review of Inflationary Cosmology|year= 2001|arxiv=hep-ph/0101119|bibcode=2001hep.ph....1119B}}</ref>

In hybrid inflation, one scalar field is responsible for most of the energy density (thus determining the rate of expansion), while another is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton would not affect inflation termination, while fluctuations in the latter would not affect the rate of expansion. Therefore, hybrid inflation is not eternal.<ref>{{Cite journal|last1=Linde|first1=Andrei|last2=Fischler|first2=W.|year=2005|title=Prospects of Inflation|journal=[[Physica Scripta]]|volume=117|issue=T117|pages=40–48|arxiv=hep-th/0402051|bibcode=2005PhST..116...56B|doi=10.1238/Physica.Topical.117a00056|s2cid=17779961}}</ref><ref>{{Cite journal|last1=Blanco-Pillado|first1=J. J.|last2=Burgess|first2=C. P.|last3=Cline|first3=J. M.|last4=Escoda|first4=C.|last5=Gomez-Reino|first5=M.|last6=Kallosh|first6=R.|last7=Linde|first7=A.|last8=Quevedo|first8=F.|year=2004|title=Racetrack Inflation|journal=[[Journal of High Energy Physics]]|volume=2004|issue=11|page=063|arxiv=hep-th/0406230|bibcode=2004JHEP...11..063B|doi=10.1088/1126-6708/2004/11/063|s2cid=12461702}}</ref> When the second (slow-rolling) inflaton reaches the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the inflaton down its potential, leading to termination of inflation.

===Relation to dark energy===
[[Dark energy]] is broadly similar to inflation and is thought to be causing the expansion of the present-day universe to accelerate. However, the energy scale of dark energy is much lower, {{10^|−12}}&nbsp;GeV, roughly 27 [[orders of magnitude]] less than the scale of inflation.

===Inflation and string cosmology===
The discovery of [[Compactification (physics)#Flux compactification|flux compactification]]s opened the way for reconciling inflation and string theory.<ref>{{Cite journal|last=Kachru|first=Shamit|display-authors=etal|date=2003|title=Towards inflation in string theory|journal=[[Journal of Cosmology and Astroparticle Physics]]|volume=2003|issue=10|page=013|arxiv=hep-th/0308055|bibcode=2003JCAP...10..013K|citeseerx=10.1.1.264.3396|doi=10.1088/1475-7516/2003/10/013|s2cid=5951592}}</ref> ''Brane inflation'' suggests that inflation arises from the motion of [[D-brane]]s<ref>{{Cite journal|last1=Dvali|first1=Gia|last2=Henry Tye|first2=S. -H.|year=1998|title=Brane Inflation|journal=[[Physics Letters B]]|volume=450|issue=1999|pages=72–82|arxiv=hep-ph/9812483|bibcode=1999PhLB..450...72D|doi=10.1016/S0370-2693(99)00132-X|s2cid=118930228}}</ref> in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by the ''Dirac–Born–Infeld action'', is different from ordinary inflation. The dynamics are not completely understood. It appears that special conditions are necessary since inflation occurs in tunneling between two vacua in the [[string landscape]]. The process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism.

===Inflation and loop quantum gravity===
When investigating the effects the theory of [[loop quantum gravity]] would have on cosmology, a [[loop quantum cosmology]] model has evolved that provides a possible mechanism for cosmological inflation. Loop quantum gravity assumes a quantized spacetime. If the energy density is larger than can be held by the quantized spacetime, it is thought to bounce back.<ref>
{{cite magazine
 |last=Bojowald |first=Martin
 |date=October 2008
 |title=Big Bang or Big Bounce?: New theory on the universe's birth
 |url=http://www.scientificamerican.com/article/big-bang-or-big-bounce/
 |access-date=2015-08-31
 |magazine=[[Scientific American]]
}}
</ref>

==Alternatives and adjuncts==
Other models have been advanced that are claimed to explain some or all of the observations addressed by inflation.

=== Big bounce ===
The big bounce hypothesis attempts to replace the cosmic singularity with a cosmic contraction and bounce, thereby explaining the initial conditions that led to the big bang. The flatness and horizon problems are naturally solved in the [[Einstein–Cartan theory|Einstein–Cartan]]–Sciama–Kibble theory of gravity, without needing an exotic form of matter or free parameters.<ref>
{{cite journal |author=Poplawski |first=N. J. |year=2010 |title=Cosmology with torsion: An alternative to cosmic inflation |journal=[[Physics Letters B]] |volume=694 |issue=3 |pages=181–185 |arxiv=1007.0587 |bibcode=2010PhLB..694..181P |doi=10.1016/j.physletb.2010.09.056}}
</ref><ref>
{{cite journal |author=Poplawski |first=N. J. |year=2012 |title=Nonsingular, big-bounce cosmology from spinor-torsion coupling |journal=[[Physical Review D]] |volume=85 |issue=10 |article-number=107502 |arxiv=1111.4595 |bibcode=2012PhRvD..85j7502P |doi=10.1103/PhysRevD.85.107502 |s2cid=118434253}}
</ref> This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the [[torsion tensor]], as a dynamical variable. The minimal coupling between torsion and [[Dirac spinor]]s generates a spin-spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction averts the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. The rapid expansion immediately after the [[Big Bounce]] explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic. As the density of the Universe decreases, the effects of torsion weaken and the Universe smoothly enters the radiation-dominated era.

=== Ekpyrotic and cyclic models ===
The [[Ekpyrotic universe|ekpyrotic]] and [[cyclic model]]s are also considered adjuncts to inflation. These models solve the [[horizon problem]] through an expanding epoch well ''before'' the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to a [[Big Crunch]]. The Universe passes through the Big Crunch and emerges in a hot [[Big Bang]] phase. In this sense they are reminiscent of [[Richard Chace Tolman]]'s [[oscillatory universe]]; in Tolman's model, however, the total age of the Universe is necessarily finite, while in these models this is not necessarily so. Whether the correct spectrum of density fluctuations can be produced, and whether the Universe can successfully navigate the Big Bang/Big Crunch transition, remains a topic of controversy and current research. Ekpyrotic models avoid the [[magnetic monopole]] problem as long as the temperature at the Big Crunch/Big Bang transition remains below the Grand Unified Scale, as this is the temperature required to produce magnetic monopoles in the first place. As things stand, there is no evidence of any 'slowing down' of the expansion, but this is not surprising as each cycle is expected to last on the order of a trillion years.<ref>{{Cite journal |last=Lehners |first=Jean-Luc |date=2 June 2009 |title=Ekpyrotic and cyclic cosmology |journal=Physics Reports |volume=465 |issue=6 |pages=223–263 |doi=10.1016/j.physrep.2008.06.001 |arxiv=0806.1245 |s2cid=17534907 }}</ref>

=== String gas cosmology ===
[[String theory]] requires that, in addition to the three observable spatial dimensions, additional dimensions exist that are curled up or [[compactification (physics)|compactified]] (see also [[Kaluza–Klein theory]]). Extra dimensions appear as a frequent component of [[supergravity]] models and other approaches to [[quantum gravity]]. This raised the contingent question of why four space-time dimensions became large and the rest became unobservably small. An attempt to address this question, called ''string gas cosmology'', was proposed by [[Robert Brandenberger]] and [[Cumrun Vafa]].<ref>
{{cite journal
 |last1=Brandenberger |first1=R.
 |last2=Vafa |first2=C.
 |year=1989
 |title=Superstrings in the early universe
 |journal=[[Nuclear Physics B]]
 |volume=316 |issue=2 |pages=391–410
 |bibcode=1989NuPhB.316..391B |citeseerx=10.1.1.56.2356
 |doi=10.1016/0550-3213(89)90037-0
}}
</ref> This model focuses on the dynamics of the early universe considered as a hot gas of strings. Brandenberger and Vafa show that a dimension of [[spacetime]] can only expand if the strings that wind around it can efficiently annihilate each other, which became known as [[Brandenberger–Vafa mechanism]]. Each string is a one-dimensional object, and the largest number of dimensions in which two strings will [[Transversality (mathematics)|generically intersect]] (and, presumably, annihilate) is three. Therefore, the most likely number of non-compact (large) spatial dimensions is three. Current work on this model centers on whether it can succeed in stabilizing the size of the compactified dimensions and produce the correct spectrum of primordial density perturbations.<ref>{{cite journal |last1=Battefeld|first1=Thorsten |last2=Watson |first2=Scott |year=2006 |title=String Gas Cosmology |journal=[[Reviews of Modern Physics]] |volume=78|issue=2|pages=435–454 |arxiv=hep-th/0510022 |bibcode=2006RvMP...78..435B |doi=10.1103/RevModPhys.78.435 |s2cid=2246186}}</ref> The original model did not "solve the entropy and flatness problems of standard cosmology",<ref>{{cite journal|last1=Brandenberger|first1=Robert H.|last2=Nayeri|first2=ALI|last3=Patil|first3=Subodh P.|last4=Vafa|first4=Cumrun|date=2007|title=String Gas Cosmology and Structure Formation|url=https://cds.cern.ch/record/978863|journal=[[International Journal of Modern Physics A]]|volume=22|issue=21|pages=3621–3642|arxiv=hep-th/0608121|bibcode=2007IJMPA..22.3621B|doi=10.1142/S0217751X07037159|s2cid=5899352}}</ref> although Brandenburger and coauthors later argued that these problems can be eliminated by implementing string gas cosmology in the context of a bouncing-universe scenario.<ref>{{Cite journal|last1=Lashkari|first1=Nima|last2=Brandenberger|first2=Robert H|date=2008-09-17|title=Speed of sound in string gas cosmology|journal=[[Journal of High Energy Physics]]|volume=2008|issue=9|page=082|doi=10.1088/1126-6708/2008/09/082|issn=1029-8479|arxiv=0806.4358|bibcode=2008JHEP...09..082L|s2cid=119184258}}</ref><ref>{{Cite journal|last1=Kamali|first1=Vahid|last2=Brandenberger|first2=Robert|date=2020-05-11|title=Creating spatial flatness by combining string gas cosmology and power law inflation|journal=[[Physical Review D]]|language=en|volume=101|issue=10|article-number=103512|doi=10.1103/PhysRevD.101.103512|arxiv=2002.09771|bibcode=2020PhRvD.101j3512K|issn=2470-0010|doi-access=free}}</ref>

=== Varying ''c'' ===
{{Further|Variable speed of light}}
Cosmological models employing a [[variable speed of light]] have been proposed to resolve the horizon problem of and provide an alternative to cosmic inflation. In the VSL models, the fundamental constant ''c'', denoting the [[speed of light]] in vacuum, is greater in the [[early universe]] than its present value, effectively increasing the [[particle horizon]] at the time of decoupling sufficiently to account for the observed isotropy of the CMB.

==Criticisms==
Since its introduction by Alan Guth in 1980, the inflationary paradigm has become widely accepted. Nevertheless, many physicists, mathematicians, and philosophers of science have voiced criticisms, claiming untestable predictions and a lack of serious empirical support.<ref name=Steinhardt2011/> In 1999, John Earman and Jesús Mosterín published a thorough critical review of inflationary cosmology, concluding,
: "we do not think that there are, as yet, good grounds for admitting any of the models of inflation into the standard core of cosmology."<ref name="Earman-Mosterín">{{cite journal |last1=Earman |first1= John |first2=Jesús |last2=Mosterín |date=March 1999 |title=A Critical Look at Inflationary Cosmology |journal= Philosophy of Science |volume=66 |issue= 1 |pages= 1–49 |jstor=188736 |doi=10.1086/392675|s2cid= 120393154 }}</ref>

As pointed out by [[Roger Penrose]] from 1986 on, in order to work, inflation requires extremely specific initial conditions of its own, so that the problem (or pseudo-problem) of initial conditions is not solved:
: "There is something fundamentally misconceived about trying to explain the uniformity of the early universe as resulting from a thermalization process. ... For, if the thermalization is actually doing anything ... then it represents a definite increasing of the entropy. Thus, the universe would have been even more special before the thermalization than after."<ref>
{{cite book
 |last=Penrose |first=Roger |author-link=Roger Penrose
 |year=2004
 |title=The Road to Reality: A Complete Guide to the Laws of the Universe
 |place=London, UK
 |publisher=Vintage Books
 |page=755}}<br/>
{{cite journal
 |last=Penrose |first=Roger |author-link=Roger Penrose
 |year=1989
 |title=Difficulties with Inflationary Cosmology
 |journal=[[Annals of the New York Academy of Sciences]]
 |volume=271 |pages=249–264
 |bibcode=1989NYASA.571..249P
 |doi=10.1111/j.1749-6632.1989.tb50513.x |s2cid=122383812
}}
</ref>

The problem of specific or "fine-tuned" initial conditions would not have been solved; it would have gotten worse. At a conference in 2015, Penrose said that
: "inflation isn't falsifiable, it's falsified. ... [[BICEP and Keck Array|BICEP]] did a wonderful service by bringing all the inflation-ists out of their shell, and giving them a black eye."<ref name="Hložek">
{{cite conference
 |last=Hložek |first=Renée
 |date=10–12 June 2015
 |title=CMB@50 day three
 |conference=Cosmic Microwave Background @50
 |place=Princeton, NJ
 |url=http://physics.princeton.edu/cmb50/home.shtml
 |access-date=15 July 2015  |archive-url=https://web.archive.org/web/20171219102718/http://physics.princeton.edu/cmb50/home.shtml
 |archive-date=19 December 2017
}} — collated remarks from the third day of the conference.
</ref>

A recurrent criticism of inflation is that the invoked inflaton field does not correspond to any known physical field, and that its [[potential energy]] curve seems to be an ad hoc contrivance to accommodate almost any data obtainable. [[Paul Steinhardt]], one of the founding fathers of inflationary cosmology, calls 'bad inflation' a period of accelerated expansion whose outcome conflicts with observations, and 'good inflation' one compatible with them:
: "Not only is bad inflation more likely than good inflation, but no inflation is more likely than either ... Roger Penrose considered all the possible configurations of the inflaton and gravitational fields. Some of these configurations lead to inflation ... Other configurations lead to a uniform, flat universe directly – without inflation. Obtaining a flat universe is unlikely overall. Penrose's shocking conclusion, though, was that obtaining a flat universe without inflation is much more likely than with inflation – by a factor of [[googolplex|10 to the googol]]{{efn|
A googol is {{10^|100}}, hence Steinhardt<ref name=Steinhardt2011/> is claiming the probability ratio is {{10^|{{10^|100}} }}.
}} power!"<ref name=Steinhardt2011>
{{cite magazine
 |last=Steinhardt |first=Paul J.  |author-link=Paul Steinhardt
 |year=2011
 |title=The inflation debate: Is the theory at the heart of modern cosmology deeply flawed?
 |magazine=[[Scientific American]]
 |volume=304 |issue=4 |pages=18–25
 |doi=10.1038/scientificamerican0411-36
 |pmid=21495480 |bibcode=2011SciAm.304d..36S
}}
</ref><ref name=SteinhardtTurok2007>
{{cite book
 |last1=Steinhardt |first1=Paul J. |author1-link=Paul Steinhardt
 |last2=Turok      |first2=Neil    |author2-link=Neil Turok
 |date=2007
 |title=Endless Universe: Beyond the Big Bang
 |publisher=Broadway Books
 |isbn=978-0-7679-1501-4
}}
</ref>
Together with Anna Ijjas and [[Abraham Loeb]], he wrote articles claiming that the inflationary paradigm is in trouble in view of the data from the [[Planck (spacecraft)|Planck satellite]].<ref name=Steinhardt2013>
{{cite journal
 |first1=Anna    |last1=Ijjas
 |first2=Paul J. |last2=Steinhardt  |author2-link=Paul Steinhardt
 |first3=Abraham |last3=Loeb        |author3-link=Abraham Loeb
 |year=2013
 |title=Inflationary paradigm in trouble after Planck 2013
 |journal=[[Physics Letters B]]
 |volume=723 |issue=4–5 |pages=261–266
 |arxiv=1304.2785 |bibcode=2013PhLB..723..261I
 |doi=10.1016/j.physletb.2013.05.023 |s2cid=14875751
}}
</ref><ref>
{{cite journal
 |first1=Anna    |last1=Ijjas 
 |first2=Paul J. |last2=Steinhardt  |author2-link=Paul Steinhardt
 |first3=Abraham |last3=Loeb        |author3-link=Abraham Loeb
 |year=2014
 |title=Inflationary schism after Planck 2013
 |journal=[[Physics Letters B]]
 |volume=736  |pages=142–146
 |arxiv=1402.6980  |bibcode=2014PhLB..736..142I
 |doi=10.1016/j.physletb.2014.07.012  |s2cid=119096427
}}
</ref>

Counter-arguments were presented by [[Alan Guth]], [[David Kaiser (physicist)|David Kaiser]], and [[Yasunori Nomura]]<ref name=GKN>
{{cite journal
 |last1=Guth   |first1=Alan H.  |author1-link=Alan Guth
 |last2=Kaiser |first2=David I. |author2-link=David Kaiser (physicist) 
 |last3=Nomura |first3=Yasunori
 |year=2014
 |title=Inflationary paradigm after Planck 2013
 |journal=[[Physics Letters B]]
 |volume=733 |pages=112–119
 |arxiv=1312.7619 |bibcode=2014PhLB..733..112G
 |doi=10.1016/j.physletb.2014.03.020 |s2cid=16669993
}}
</ref> and by Linde,<ref>
{{cite conference
 |last=Linde |first=Andrei |author-link=Andrei Linde
 |date=8 July – 2 August 2013
 |title=Inflationary cosmology after Planck 2013
 |at=session&nbsp;C
 |location=Oxford, UK
 |conference=Post-Planck Cosmology: École de physique des Houches
 |publication-date=2015
 |publisher=Ecole d'été de physique théorique / Oxford University Press
 |isbn=978-0-19-872885-6
}}
</ref> saying that
: "cosmic inflation is on a stronger footing than ever before".<ref name=GKN/>

==See also==
{{div col |colwidth=15em |content=

* [[Brane cosmology]]
* [[Angular momentum#Conservation of angular momentum|Conservation of angular momentum]]
* [[Cosmology]]
* [[Dark flow]]
* [[Hubble's law]]
* [[Non-minimally coupled inflation]]
* [[Nonlinear optics]]
* [[3-torus|Three-torus model of the universe]]
* [[Warm inflation]]

}} <!-- end "content=" -->

==Notes==
{{notelist}}

==References==
{{reflist|25em}}

==Sources==
{{refbegin|20em|small=yes}}
* {{cite book
 |first=Alan |last=Guth  |author-link=Alan Guth
 |year=1997
 |title=The Inflationary Universe: The quest for a new theory of cosmic origins
 |title-link=The Inflationary Universe
 |publisher=Perseus
 |isbn=978-0-201-32840-0
}}
* {{cite book
 |first=Stephen |last=Hawking |author-link=Stephen Hawking
 |year=1998
 |title=A Brief History of Time
 |title-link=A Brief History of Time
 |publisher=Bantam 
 |isbn=978-0-553-38016-3
}}
* {{cite book
 |first1=Stephen |last1=Hawking   |author1-link=Stephen Hawking
 |first2=Gary   |last2=Gibbons  |author2-link=Gary Gibbons
 |year=1983
 |title=The Very Early Universe
 |publisher=Cambridge University Press
 |isbn=978-0-521-31677-4
}}
* {{cite book
 |first1=Edward  |last1=Kolb
 |first2=Michael |last2=Turner
 |year=1988
 |title=The Early Universe
 |publisher=Addison-Wesley
 |isbn=978-0-201-11604-5
}}
* {{Cite book |last=Linde |first=Andrei |author-link=Andrei Linde |arxiv=hep-th/0503203 |title=Particle Physics and Inflationary Cosmology |publisher=Harwood |location=Chur, Switzerland |date=1990 |isbn=3-7186-0490-6|bibcode = 2005hep.th....3203L }}
* {{cite book
 |last=Linde |first=Andrei |author-link=Andrei Linde
 |year=2005
 |title=Particle Physics and Inflationary Cosmology
 |series=Contemporary Concepts in Physics  |volume=5
 |isbn=978-3-7186-0490-6  |arxiv=hep-th/0503203
 |bibcode = 2005hep.th....3203L
}}
* {{cite journal
 |last=Linde |first=Andrei  |author-link=Andrei Linde
 |year=2006
 |title=Inflation and String Cosmology
 |journal=Progress of Theoretical Physics Supplement
 |volume=163  |pages=295–322
 |arxiv=hep-th/0503195  |doi=10.1143/PTPS.163.295
 |bibcode=2006PThPS.163..295L  |s2cid=119410403
}}
* {{cite book
 |first1=Andrew |last1=Liddle
 |first2=David  |last2=Lyth
 |year=2000
 |title=Cosmological Inflation and Large-Scale Structure
 |publisher=Cambridge
 |isbn=978-0-521-57598-0
}}
* {{cite journal
 |first1=David H. |last1=Lyth
 |first2=Antonio  |last2=Riotto
 |year=1999
 |title=Particle physics models of inflation and the cosmological density perturbation
 |journal= Physics Reports
 |volume=314  |issue=1–2  |pages=1–146
 |arxiv=hep-ph/9807278   |bibcode=1999PhR...314....1L
 |doi=10.1016/S0370-1573(98)00128-8  |s2cid=119517140
}}
* {{cite book
 |first=Viatcheslav |last=Mukhanov
 |year=2005
 |title=Physical Foundations of Cosmology
 |publisher=Cambridge University Press
 |isbn=978-0-521-56398-7
}}
* {{cite book |first=Alex |last=Vilenkin |author-link=Alex Vilenkin
 |year=2006
 |title=Many Worlds in One: The search for other universes
 |publisher=Hill and Wang
 |isbn=978-0-8090-9523-0
 |url=https://archive.org/details/manyworldsinoneo00vile
 |via=archive.org
}}
* {{cite book
 |first=P.J.E. |last=Peebles |author-link=Philip James Edwin Peebles
 |year=1993
 |title=Principles of Physical Cosmology
 |publisher=Princeton University Press
 |isbn=978-0-691-01933-8
 |url=https://archive.org/details/principlesofphys00pjep
 |via=archive.org
}}
* {{cite book |last=Smeenk |first=Chris |title=False Vacuum: Early Universe Cosmology and the Development of Inflation |others=In: The Universe of General Relativity (Einstein Studies, Book 11) |editor-last1=Kox |editor-first1=A.J. |editor-last2=Eisenstaedt |editor-first2=Jean 
 |isbn=978-0-8176-4380-5
 |publisher=Birkhäuser Boston |year=2005 |pages=223–257 }}
{{refend}}

==External links==
{{wikiquote}}
* {{Cite web |last=John R. |first=Gribbin |author-link=John Gribbin |title=Inflation for Beginners |url=https://aether.lbl.gov/www/science/inflation-beginners.html |access-date=2025-11-16 |website=aether.lbl.gov}}
* [http://nedwww.ipac.caltech.edu/level5/Guth/Guth_contents.html Was Cosmic Inflation The 'Bang' Of The Big Bang?], by Alan Guth, 1997
* {{cite arXiv <!-- -->|arxiv=astro-ph/9901124 |author1=Andrew R Liddle |title=An introduction to cosmological inflation |page=260 |year=1999}}
* [https://web.archive.org/web/20041120175509/http://www2.iap.fr/Conferences/Colloque/col2004/Docs/20040628_liddle.pdf update 2004] by Andrew Liddle
* {{cite arXiv <!-- -->|arxiv=hep-ph/0309238 |last1=Covi |first1=Laura |title=Status of observational cosmology and inflation |page=67 |year=2003}}
* {{cite arXiv <!-- -->|arxiv=hep-th/0311040 |last1= Lyth |first1= David H. |title= Which is the best inflation model? |page= 260 |year= 2003}}
* [https://web.archive.org/web/20061002183844/http://www.symmetrymag.org/cms/?pid=1000045 The Growth of Inflation] ''Symmetry'', December 2004
* [https://web.archive.org/web/20061002193415/http://www.symmetrymag.org/cms/?pid=1000037 Guth's logbook showing the original idea]
* [https://archive.today/20121216135256/http://skyandtelescope.com/news/article_1697_1.asp WMAP Bolsters Case for Cosmic Inflation, March 2006]
* [http://www.nasa.gov/home/hqnews/2006/mar/HQ_06097_first_trillionth_WMAP.html NASA March 2006 WMAP press release] {{Webarchive|url=https://web.archive.org/web/20131122192419/http://www.nasa.gov/home/hqnews/2006/mar/HQ_06097_first_trillionth_WMAP.html |date=22 November 2013 }}
* [[Max Tegmark]]. ''[[Our Mathematical Universe]]'' (2014), [http://space.mit.edu/home/tegmark/pdf/inflation_excerpt.pdf "Chapter 5: Inflation"]

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