Editing Cosmic inflation (section)

==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|page=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|page=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 |pages=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|pages=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|pages=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|pages=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|pages=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|pages=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>