Editing Cosmic inflation (section)

==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.

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  |page=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=9781402030406
 |url=https://books.google.com/books?id=3UXak_7yR3MC&pg=PA88
}}
</ref>
}}

===Slow-roll inflation===
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''). 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.

===Effects of asymmetries===
{{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>