View source for Inflaton

{{short description|Hypothetical field that may have driven cosmic inflation}}
{{About|a particle/quantum field posited in cosmology|a general rise in the level of prices|Inflation|other uses of "inflation"|Inflation (disambiguation)}}
{{distinguish|Instanton}}

The '''inflaton field''' is a hypothetical [[Scalar field theory|scalar field]] that is conjectured to have driven [[Inflation (cosmology)|cosmic inflation]] in the [[very early universe]].<ref name=Guth1997>
{{cite book
 |last=Guth |first=Alan H.  |author-link=Alan Guth
 |year=1997
 |title=The Inflationary Universe: The quest for a new theory of cosmic origins
 |publisher=[[Basic Books]]
 |isbn=978-0-2013-2840-0
 |pages=[https://archive.org/details/inflationaryuniv0000guth/page/233 233]–234
 |url=https://archive.org/details/inflationaryuniv0000guth
 |via=[[Internet Archive]] (archive.org) |url-access=registration
}}
</ref><ref>
{{cite book
 |last1=Steinhardt  |first1=Paul J.  |author1-link=Paul Steinhardt
 |last2=Turok       |first2=Neil     |author2-link=Neil Turok
 |year=2007
 |title=Endless Universe: Beyond the bang
 |page=114
 |publisher=[[Random House]]
 |isbn=978-0-7679-1501-4
 |url=https://books.google.com/books?id=Jp6gJCuvj-kC&pg=PA114
 |via=Google
}}
</ref><ref>
{{cite magazine
 |last=Steinhardt  |first=Paul J.  |author-link=Paul Steinhardt
 |date=April 2011
 |title=Inflation debate: Is the theory at the heart of modern cosmology deeply flawed?
 |magazine=[[Scientific American]]
 |url=http://www.physics.princeton.edu/~steinh/0411036.pdf
 |via=physics.princeton.edu  |url-status=dead  |access-date=2013-12-31
 |archive-url=https://web.archive.org/web/20140824094646/http://www.physics.princeton.edu/~steinh/0411036.pdf
 |archive-date=2014-08-24
}}
</ref> The field, originally postulated by [[Alan Guth]],<ref name=Guth1997/> provides a mechanism that can generate a period of rapid [[metric expansion of space|expansion]] from {{10^|−35}} to {{nobr|{{10^|−34}} [[second]]s}} after the [[Big Bang|initial expansion]], which consequently forms a universe consistent with observed spatial [[isotropy]] and [[homogeneity]].

== Cosmological inflation ==
{{main|Inflation (cosmology)}}

The basic{{clarify|date=October 2016}} model of inflation proceeds in three phases:<ref>
{{cite arXiv
 |last=Tsujikawa |first=Shinji
 |year=2003
 |title=Introductory review of cosmic inflation
 |eprint=hep-ph/0304257
}}
</ref>
* Expanding vacuum state with high potential energy
* [[Phase transition]] to true vacuum
* Slow roll and reheating

=== Expanding vacuum state with high potential energy ===

A ''"vacuum"'' or ''"[[vacuum state]]"'' in [[quantum field theory]] is a state of quantum fields that is at [[local minimum|locally minimal]] potential energy. Quantum particles are excitations that deviate from this minimal potential energy state, therefore a vacuum state has no particles in it. Depending on the specifics of a quantum field theory, there can be more than one vacuum state. Those different vacua, despite all "being empty" (having no particles), will generally each have different [[vacuum energy|vacuum energies]]. Quantum field theory stipulates that the pressure of the vacuum energy is always negative and equal in magnitude to its energy density.

Inflationary theory postulates that there is some vacuum state with very large vacuum energy, caused by a non-zero vacuum expectation value of the inflaton field. Any region of space in this state will rapidly expand. Even if initially it is not empty (contains some particles), very rapid exponential expansion dilutes any particles that might have previously been present to essentially zero density.

=== Transition to true vacuum ===
Inflationary theory further postulates that this "inflationary vacuum" state is not the state with globally the lowest energy; rather, it is a "[[false vacuum]]", also known as a ''[[metastable]]'' state.<ref>
{{cite book
 |last1=Peter |first1=Patrick
 |last2=Uzan |first2=Jean-Philippe
 |last3=Peter |first3=Patrick
 |year=2013
 |title=Primordial Cosmology |edition=[[paperback|ppb]] 1st
 |publisher=Oxford University Press
 |location=Oxford, UK
 |isbn=978-0-19-966515-0
 |series=Oxford graduate texts
 |at=Chapter&nbsp;8
}}
</ref>

Historically, the first proposals of inflation<ref>
{{cite journal
 |last=Guth |first=Alan H. |author-link=Alan Guth
 |date=15 January 1981
 |title=Inflationary universe: A possible solution to the horizon and flatness problems
 |journal=Physical Review D
 |volume=23 |issue=2 |pages=347–356
 |doi=10.1103/PhysRevD.23.347
 |bibcode=1981PhRvD..23..347G
}}
</ref> suggested that the transition from the "false" to the "true vacuum" follows a [[quantum tunnelling]] process, where the inflaton field passes through the potential barrier of the two phases (this would correspond to a [[first-order phase transition]]). However, it was realised<ref>
{{cite journal
 |last1=Guth |first1=Alan H. |author1-link=Alan Guth
 |last2=Weinberg |first2=Erick J.
 |year=1983 |title=Could the universe have recovered from a slow first-order phase transition?
 |journal=[[Nuclear Physics (journal)|Nuclear Physics B]] |lang=en
 |volume=212 |issue=2 |pages=321–364
 |doi=10.1016/0550-3213(83)90307-3
 |bibcode=1983NuPhB.212..321G
}}</ref> that this procedure would create a very inhomogeneous Universe on the large scales, contrary to what we observe.[[File:Falsevacuum.svg|thumb|Example of a field with a "false vacuum". Similar potentials had been considered for inflation. Note however that the simple, "slow-roll" potential has a smoother transition between the "false" and "true vacuum".|253x253px]]The theory was soon refined<ref>
{{cite journal
 |last=Linde |first=A.D.
 |year=1982
 |title=A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems
 |journal=Physics Letters B |lang=en
 |volume=108 |issue=6 |pages=389–393
 |doi=10.1016/0370-2693(82)91219-9
 |bibcode=1982PhLB..108..389L
}}
</ref><ref>
{{cite journal
 |last1=Albrecht |first1=Andreas
 |last2=Steinhardt |first2=Paul J.
 |date=26 April 1982
 |title=Cosmology for grand unified theories with radiatively induced symmetry breaking
 |journal=[[Physical Review Letters]]
 |volume=48 |issue=17 |pages=1220–1223
 |doi=10.1103/PhysRevLett.48.1220
 |bibcode=1982PhRvL..48.1220A
}}
</ref> to allow a smooth transition between the two phases, where the inflaton field "rolls down" its potential.

=== Slow roll and reheating ===
In simple, modern models of inflation, the inflaton originally has much bigger potential energy than kinetic energy ("slow-roll"), which leads the inflationary potential to act as an effective [[cosmological constant]]. As an effect, one expects a period of exponential expansion.

When the inflaton reaches its true vacuum, it needs to be connected to the standard cosmological model. At that point, the field has "lost" its original potential energy, but gained kinetic energy. To introduce the standard model at this point, the idea is that this energy needs to be transferred to the observed Standard Model particles.<ref>
{{cite journal
 |last1=Kofman |first1=Lev
 |last2=Linde  |first2=Andrei
 |last3=Starobinsky |first3=Alexei
 |date=12 October 1994
 |title=Reheating after inflation
 |journal=[[Physical Review Letters]]
 |volume=73 |issue=24 |pages=3195–3198
 |arxiv=hep-th/9405187 |pmid=10057315
 |bibcode=1994PhRvL..73.3195K
 |doi=10.1103/PhysRevLett.73.3195
}}
</ref><ref>
{{cite report
 |first=Daniel |last=Baumann
 |date=December 2011
 |title=The Physics of Inflation
 |url=https://www.icts.res.in/sites/default/files/baumann_icts_dec2011.pdf
 |via=icts.res.in
}}
</ref> This procedure is known as "reheating". When complete, the Universe is [[Radiation-dominated|radiation dominated]] and its expansion decelerates. The decay of the inflaton fills the space with new particles, which interact with each other and finally reach the hot and dense state of the [[Big Bang|Big Bang theory]].<ref>
{{cite web
 |last=Strassler |first=Matt
 |date=17 March 2014
 |title=Inflation
 |department=History of the Universe
 |series=Relativity, space, astronomy, and cosmology
 |website=Of Particular Significance (profmattstrassler.com)
 |type=blog  |lang=en-US
 |url=https://profmattstrassler.com/articles-and-posts/relativity-space-astronomy-and-cosmology/history-of-the-universe/inflation/
 |access-date=3 August 2024  |df=dmy-all
 |quote=... by the author of ''Waves in an Impossible Sea''.
}}
</ref>

== Field quanta ==
Just like every other quantum field, excitations of the inflaton field are expected to be quantized. The field quanta of the inflaton field are known as '''inflatons'''. Depending on the modeled potential energy density, the inflaton field's [[ground state]] might, or might not, be zero.

The term ''inflaton'' follows the typical style of other quantum particles’ names – such as [[photon]], [[gluon]], [[boson]], and [[fermion]] – deriving from the word ''inflation''. The term was first used in a paper by {{harvp|Nanopoulos|Olive|Srednicki|1983}}.<ref>
{{cite journal
 |last1=Nanopoulos |first1=D.V. |author1-link=Dimitri Nanopoulos
 |last2=Olive      |first2=D.A. |author2-link=Keith Olive
 |last3=Srednicki  |first3=M.  <!-- |author3-link=Mark Srednicki -->
 |year=1983
 |title=After primordial inflation
 |journal=[[Physics Letters B]]
 |volume=127  |issue=1–2  |pages=30–34
 |doi=10.1016/0370-2693(83)91624-6
 |bibcode=1983PhLB..127...30N
|url=http://cds.cern.ch/record/144126 }}
</ref>
The nature of the inflaton field is currently not known. One of the obstacles for narrowing its properties is that current quantum theory is not able to correctly predict the current observed vacuum energy, based on the particle content of a chosen theory (see [[Cosmological constant problem|vacuum catastrophe]]).

The confirmation of the [[Higgs boson]] led to the suggestion that it is possible that no new field is necessary – that a modified version of the [[Higgs field]] could suffice.<ref>
{{cite journal
 |last1=Bezrukov |first1=Fedor
 |last2=Shaposhnikov |first2=Mikhail
 |date=24 January 2008
 |title=The Standard Model Higgs boson as the inflaton
 |journal=Physics Letters B
 |volume=659  |issue=3  |pages=703–706
 |doi=10.1016/j.physletb.2007.11.072
 |issn=0370-2693  |arxiv=0710.3755
 |bibcode=2008PhLB..659..703B
}}
</ref> However this early proposal and others that followed have faced criticism on fundamental grounds.<ref>
{{cite journal
 |last1=Atkins |first1=Michael
 |last2=Calmet |first2=Xavier
 |date=2011-02-21
 |title=Remarks on Higgs inflation
 |journal=Physics Letters B
 |volume=697  |issue=1  |pages=37–40
 |doi=10.1016/j.physletb.2011.01.028
 |issn=0370-2693  |arxiv=1011.4179
 |bibcode=2011PhLB..697...37A
}}
</ref><ref>
{{cite web
 |last=Atkins |first=Michael
 |year=2011
 |title=Could the Higgs boson be the inflaton?
 |type=presentation slides
 |publisher=[[CERN]]
 |place=[[Meyrin]], CH
 |url=http://indico.cern.ch/event/180122/material/slides/0.pdf
 |via=[[CERN|cern.ch]]
}}
</ref>

== Non-minimally coupled inflation <!--'Non-minimally coupled inflation' redirects here--> ==
'''Non-minimally coupled inflation'''<!--boldface per WP:R#PLA--> is an [[cosmic inflation|inflationary]] model in which the constant which couples [[gravity]] to the [[inflaton field]] is not small. The [[coupling constant]] is usually represented by <math>\ \xi\ </math> (Greek letter [[xi (letter)|{{mvar|xi}}]]), which features in the [[action (physics)|action]] (constructed by modifying the [[Einstein–Hilbert action]]):<ref name=hertzberg12>
{{cite journal
 |last=Hertzberg |first=Mark P.
 |date=2010
 |title=On inflation with non-minimal coupling
 |journal=[[Journal of High Energy Physics]]
 |volume=2010  |issue=11  |article-number=23  |pages=1–2
 |arxiv=1002.2995  |bibcode=2010JHEP...11..023H
 |doi=10.1007/JHEP11(2010)023  |s2cid=54886582
}}
</ref><!-- {{rp|style=ama|p=1&ndash;2}} -->
: <math>S = \int\sqrt{ -g ~}\ \Bigl[\ \tfrac{ 1 }{ 2 } m_P^2 R - \tfrac{ 1 }{ 2 }\ \partial^{\mu}\phi ~ \partial_{\mu}\phi 
- V(\phi) - \tfrac{ 1 }{ 2 } \xi\ R\ \phi^2\ \Bigr] \operatorname{d}^4x\ ,</math>
with <math>\ \xi\ </math> representing the strength of the interaction between the curvature of space-time <math>\ R\ ,</math> and the magnitude of the inflaton field <math>\ \phi ~.</math>

== See also ==
* [[Hubble's law]]
* [[Big Bang]]
* [[Cosmological constant]]
* [[Dark energy#Inflationary dark energy|Inflationary dark energy]]
* [[List of hypothetical particles]]

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

{{particles}}

[[Category:Inflation (cosmology)]]
[[Category:Hypothetical particles]]
[[Category:Dark energy]]