Editing Cosmic inflation (section)

== Theory ==
{{See also|Expansion of the universe}}

An expanding universe generally has a [[Cosmological horizon#Cosmological horizon|cosmological horizon]], which, by analogy with the more familiar [[horizon]] caused by the curvature of [[Earth]]'s surface, marks the boundary of the part of the Universe that an observer can see. Light (or other radiation) emitted by objects beyond the cosmological horizon in an [[accelerating expansion of the universe|accelerating universe]] never reaches the observer, because the space in between the observer and the object is expanding too rapidly.

[[File:History of the Universe.svg|thumb|upright=2.3|History of the [[Universe]] – [[gravitational wave]]s are hypothesized to arise from cosmic inflation, a phase of [[accelerated expansion]] just after the [[Big Bang]].<ref name="BICEP2-2014">{{cite web |author=Staff |title=BICEP2 2014 Results Release |url=http://bicepkeck.org |date=17 March 2014 |work=[[National Science Foundation]] |access-date=18 March 2014 }}</ref><ref name="NASA-20140317">{{cite web |last=Clavin |first=Whitney |title=NASA Technology Views Birth of the Universe |url=http://www.jpl.nasa.gov/news/news.php?release=2014-082 |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>]]

The [[observable universe]] is one ''causal patch'' of a much larger unobservable universe; other parts of the Universe cannot communicate with Earth yet. These parts of the Universe are outside our current cosmological horizon, which is believed to be 46 billion light years in all directions from Earth.<ref>{{cite magazine |last=Crane |first=Leah |date=29 June 2024 |title=How big is the universe, really? |magazine=[[New Scientist]] |page=31 <!-- omit magazine & journal editors --- |editor-last=de Lange |editor-first=Catherine --> }}</ref> In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view.<ref>{{cite book |last=Saul |first=Ernest |year=2013 |title=The Coded Universe: The path to eternity |publisher=Dorrance Publishing |isbn=978-1434969057 |page=65 |url=https://books.google.com/books?id=E22mj8ImiKwC&pg=PA65 |access-date=2019-07-14 }}</ref> Yet as a local observer sees such a region for the first time, it looks no different from any other region of space the local observer has already seen: Its background radiation is at nearly the same temperature as the background radiation of other regions, and its space-time curvature is evolving lock-step with the others. This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They could not have learned it by getting signals, because they were not previously in communication with our past [[light cone]].<ref name="tiny">{{cite AV media |title=Using tiny particles to answer giant questions |series=Science Friday |date=3 April 2009 |publisher=[[National Public Radio]] |medium=audio transcript |url=https://www.npr.org/templates/story/story.php?storyId=102715275 }}</ref><ref>See also [[Faster than light#Universal expansion]].</ref>

Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or [[cosmological constant]]. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the [[Observable universe#Horizons|cosmological horizon]] is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communication. The spatial slices are expanding very fast to cover huge volumes. Things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous.

As the inflationary field slowly relaxes to the vacuum, the cosmological constant goes to zero and space begins to expand normally. The new regions that come into view during the normal expansion phase are exactly the same regions that were pushed out of the horizon during inflation, and so they are at nearly the same temperature and curvature, because they come from the same originally small patch of space.

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===
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 essentially because the cosmological horizon is no different from a black-hole horizon, except for not testable disagreements about what is on the other side. The 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.{{efn|
Not only is inflation very effective at driving down the number density of magnetic monopoles, it is also effective at driving down the number density of every other type of particle, including photons.<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|style=ama|p= 202–207}}
}}

===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-year=1st ed. 1983
 |isbn=9780521316774
 |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>