Editing Cosmic inflation (section)

===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.