Editing Cosmic inflation (section)

==Observational status==
Inflation is a mechanism for realizing the [[cosmological principle]], which is the basis of the standard model of physical cosmology: it accounts for the homogeneity and isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the [[cosmic microwave background]] made by the [[Planck (spacecraft)|Planck spacecraft]].<ref name=":0">{{Cite journal |collaboration=Planck Collaboration |last1=Ade |first1=P.A.R. |display-authors=etal |date=2016-10-01 |title=Planck 2015 results. XIII. Cosmological parameters |journal=Astronomy & Astrophysics |volume=594 |pages=A13 |doi=10.1051/0004-6361/201525830 |issn=0004-6361 |bibcode=2016A&A...594A..13P |arxiv=1502.01589|s2cid=119262962 }}</ref> This analysis shows that the Universe is flat to within {{sfrac| 1 |2}} percent, and that it is homogeneous and isotropic to one part in 100,000.

Inflation predicts that the structures visible in the Universe today formed through the [[gravitational collapse]] of perturbations that were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations, called a [[Scale invariance#Cosmology|nearly-scale-invariant]] [[Gaussian random field]] is very specific and has only two free parameters. One is the amplitude of the spectrum and the ''[[spectral index]]'', which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealized [[de Sitter universe]]).{{efn|
Perturbations can be represented by [[Fourier modes]] of a [[wavelength]]. Each Fourier mode is [[Normal distribution|normally distributed]] (usually called Gaussian) with mean zero. Different Fourier components are uncorrelated. The variance of a mode depends only on its wavelength in such a way that within any given volume each wavelength contributes an equal amount of [[Spectral density|power]] to the spectrum of perturbations. Since the Fourier transform is in three dimensions, this means that the variance of a mode goes as 1/{{mvar|k}}{{sup|3}} to compensate for the fact that within any volume, the number of modes with a given wavenumber {{mvar|k}} goes as {{mvar|k}}{{sup|3}}.
}}
The other free parameter is the tensor to scalar ratio. The simplest inflation models, those without [[Fine-tuned universe|fine-tuning]], predict a [[Tensor field|tensor]] to scalar ratio near 0.1&nbsp;.<ref name="boyle2">{{cite journal |last1=Boyle |first1=Latham A. |last2=Steinhardt |first2=Paul J. |author2-link=Paul Steinhardt |last3=Turok |first3=Neil |author3-link=Neil Turok |date=2006-03-24 |title=Inflationary Predictions for Scalar and Tensor Fluctuations Reconsidered |journal=[[Physical Review Letters]] |volume=96 |issue=11 |pages=111301 |arxiv=astro-ph/0507455 |bibcode=2006PhRvL..96k1301B |doi=10.1103/PhysRevLett.96.111301 |pmid=16605810 |s2cid=10424288}}</ref>

Inflation predicts that the observed perturbations should be in [[thermal equilibrium]] with each other (these are called ''[[adiabatic]]'' or ''[[Isentropic process|isentropic]]'' perturbations). This structure for the perturbations has been confirmed by the [[Planck (spacecraft)|Planck spacecraft]], [[Wilkinson Microwave Anisotropy Probe|WMAP]] spacecraft and other cosmic microwave background (CMB) experiments, and [[galaxy survey]]s, especially the ongoing [[Sloan Digital Sky Survey]].<ref name=sdss2>{{cite journal |last1=Tegmark |first1=Max |display-authors=etal |date=August 2006 |title=Cosmological constraints from the SDSS luminous red galaxies |journal=[[Physical Review D]] |volume=74 |issue=12 |pages=123507 |arxiv=astro-ph/0608632 |bibcode=2006PhRvD..74l3507T |doi=10.1103/PhysRevD.74.123507 |s2cid=1368964 |hdl=1811/48518}}</ref> These experiments have shown that the one part in 100,000&nbsp;inhomogeneities observed have exactly the form predicted by theory. There is evidence for a slight deviation from scale invariance. The ''[[spectral index]]'', {{mvar|n}}{{sub|s}} is one for a scale-invariant Harrison–Zel'dovich spectrum. The simplest inflation models predict that {{mvar|n}}{{sub|s}} is between 0.92 and 0.98&nbsp;.<ref name=myths2>{{cite journal |last=Steinhardt |first=Paul J. |author2-link=Paul Steinhardt |date=2004 |title=Cosmological perturbations: Myths and facts |journal=[[Modern Physics Letters A]] |volume=19 |issue=13 & 16 |pages=967–982 |bibcode=2004MPLA...19..967S |doi=10.1142/S0217732304014252 |s2cid=42066874}}</ref><ref name="boyle2"/><ref name=tegmark2>{{cite journal |last=Tegmark |first=Max |date=2005 |title=What does inflation really predict?|journal=[[Journal of Cosmology and Astroparticle Physics]] |volume=2005 |issue=4 |page=001 |arxiv=astro-ph/0410281 |bibcode=2005JCAP...04..001T |doi=10.1088/1475-7516/2005/04/001 |s2cid=17250080 }}</ref>{{efn|
This is known as a "red" spectrum, in analogy to [[redshift]], because the spectrum has more power at longer wavelengths.
}} This is the range that is possible without [[Fine-tuned universe|fine-tuning]] of the parameters related to energy.<ref name=tegmark2/> From Planck data it can be inferred that {{mvar|n}}{{sub|s}}=0.968 ± 0.006,<ref name=":0"/><ref>{{cite journal |last1=Ade |first1=P.A.R. |collaboration=Planck Collaboration |date=October 2016 |title=Planck 2015 results. XX.&nbsp;Constraints on inflation |journal=[[Astronomy & Astrophysics]] |volume=594 |page=A20 |doi=10.1051/0004-6361/201525898 |issn=0004-6361 |bibcode=2016A&A...594A..20P |arxiv=1502.02114|s2cid=119284788 }}</ref> and a [[Tensor field|tensor]] to scalar ratio that is less than 0.11&nbsp;. These are considered an important confirmation of the theory of inflation.<ref name="wmap2"/>

Various inflation theories have been proposed that make radically different predictions, but they generally have much more [[Fine-tuning (physics)|fine-tuning]] than should be necessary.<ref name=myths2/><ref name=boyle2/> As a physical model, however, inflation is most valuable in that it robustly predicts the initial conditions of the Universe based on only two adjustable parameters: the spectral index (that can only change in a small range) and the amplitude of the perturbations. Except in contrived models, this is true regardless of how inflation is realized in particle physics.

Occasionally, effects are observed that appear to contradict the simplest models of inflation. The first-year [[Wilkinson Microwave Anisotropy Probe|WMAP]] data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature.<ref>{{cite journal|last1=Spergel |first1=D.N. |display-authors=etal |date=2003 |title=First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters |journal=[[Astrophysical Journal Supplement Series]] |volume=148 |issue=1 |pages=175–194 |arxiv=astro-ph/0302209 |bibcode=2003ApJS..148..175S |doi=10.1086/377226 |s2cid=10794058 }}</ref> However, the third-year data revealed that the effect was a statistical anomaly.<ref name=wmap2/> Another effect remarked upon since the first cosmic microwave background satellite, the [[Cosmic Background Explorer]] is that the amplitude of the [[quadrupole moment]] of the CMB is unexpectedly low and the other low multipoles appear to be preferentially aligned with the [[plane of the ecliptic|ecliptic plane]]. Some have claimed that this is a signature of [[non-Gaussianity]] and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to quantum corrections or new physics, foreground contamination, or even [[publication bias]].<ref>See [[Cosmic microwave background#Anomalies]] for details and references.</ref>

An experimental program is underway to further test inflation with more precise CMB measurements. In particular, high precision measurements of the so-called "B-modes" of the [[Cosmic microwave background radiation#Polarization|polarization]] of the background radiation could provide evidence of the [[gravitational radiation]] produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models ({{10^|15}}~{{10^|16}} [[GeV]]) is correct.<ref name=boyle2/><ref name=tegmark2/> In March 2014, the [[BICEP2]] team announced B-mode CMB polarization confirming inflation had been demonstrated. The team announced the tensor-to-scalar power ratio {{mvar|r}} was between 0.15 and 0.27 (rejecting the [[null hypothesis]]; {{mvar|r}} is expected to be 0 in the absence of inflation).<ref name="five years">{{cite journal |last1=Grant |first1=Andrew |title=Five years after BICEP2 |journal=[[Physics Today]] |date=2019 |issue=3 |page=30948 |doi=10.1063/PT.6.3.20190326a |bibcode=2019PhT..2019c0948G |s2cid=241938983 }}</ref> However, on 19 June 2014, lowered confidence in confirming the findings was reported;<ref name=PRL-20140619>{{cite journal |last1=Ade |first1=P.A.R. |collaboration=BICEP2 Collaboration |title=Detection of B-mode polarization at degree angular scales by BICEP2 |date=19 June 2014 |journal=[[Physical Review Letters]] |volume=112 |issue=24 |page=241101 |doi=10.1103/PhysRevLett.112.241101 |arxiv=1403.3985 |bibcode=2014PhRvL.112x1101B |display-authors=etal |pmid=24996078|s2cid=22780831 }}</ref><ref name=NYT-20140619>{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=19 June 2014 |title=Astronomers hedge on Big Bang detection claim |newspaper=[[The New York Times]] |url=https://www.nytimes.com/2014/06/20/science/space/scientists-debate-gravity-wave-detection-claim.html |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2014/06/20/science/space/scientists-debate-gravity-wave-detection-claim.html |archive-date=2022-01-01 |url-access=limited |access-date=20 June 2014 }}{{cbignore}}</ref><ref name="BBC-20140619">{{cite news |last=Amos |first=Jonathan |date=19 June 2014 |title=Cosmic inflation: Confidence lowered for Big Bang signal |series=[[BBC News]] |url=https://www.bbc.com/news/science-environment-27935479 |access-date=20 June 2014 }}</ref> on 19 September 2014, a further reduction in confidence was reported<ref name=AXV-20140919>{{cite journal |last1=Ade |first1=P.A.R. |collaboration=Planck Collaboration Team |year=2016 |title=Planck intermediate results. XXX.&nbsp;The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes |journal=Astronomy & Astrophysics |volume=586 |issue=133 |page=A133 |arxiv=1409.5738 |doi=10.1051/0004-6361/201425034 |bibcode=2016A&A...586A.133P |s2cid=9857299 }}</ref><ref name=NYT-20140922>{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=22 September 2014 |title=Study confirms criticism of Big Bang finding |newspaper=[[The New York Times]] |url=https://www.nytimes.com/2014/09/23/science/space/study-confirms-criticism-of-big-bang-finding.html |url-access=limited |access-date=22 September 2014 |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2014/09/23/science/space/study-confirms-criticism-of-big-bang-finding.html |archive-date=2022-01-01 }}{{cbignore}}</ref> and, on 30 January 2015, even less confidence yet was reported.<ref name="NASA-20150130">{{cite press release |last=Clavin |first=Whitney |date=30 January 2015 |title=Gravitational waves from early universe remain elusive |publisher=[[NASA]] |url=http://www.jpl.nasa.gov/news/news.php?release=2015-46 |access-date=30 January 2015 }}</ref><ref name=NYT-20150130>{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=30 January 2015 |title=Speck of interstellar dust obscures glimpse of Big Bang |newspaper=[[The New York Times]] |url=https://www.nytimes.com/2015/01/31/us/a-speck-of-interstellar-dust-rebuts-a-big-bang-theory.html |url-access=limited |access-date=31 January 2015 |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2015/01/31/us/a-speck-of-interstellar-dust-rebuts-a-big-bang-theory.html |archive-date=2022-01-01 }}{{cbignore}}</ref> By 2018, additional data suggested, with 95% confidence, that <math>r</math> is 0.06 or lower: Consistent with the null hypothesis, but still also consistent with many remaining models of inflation.<ref name="five years"/>

Other potentially corroborating measurements are expected from the [[Planck (spacecraft)|Planck spacecraft]], although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere.<ref>
{{cite conference
 |first1=C. |last1=Rosset
 |collaboration=PLANCK-HFI collaboration
 |year=2005
 |title=Systematic effects in CMB polarization measurements
 |book-title=Exploring the Universe: Contents and structures of the universe
 |conference=XXXIXth Rencontres de Moriond
 |arxiv=astro-ph/0502188
}}
</ref>
Other forthcoming measurements, such as those of [[21 centimeter radiation]] (radiation emitted and absorbed from neutral hydrogen before the [[population III star|first stars]] formed), may measure the power spectrum with even greater resolution than the CMB and galaxy surveys, although it is not known if these measurements will be possible or if interference with [[radio frequency|radio sources]] on Earth and in the galaxy will be too great.<ref>
{{cite journal
 |first1=A. |last1=Loeb
 |first2=M. |last2=Zaldarriaga
 |year=2004
 |title=Measuring the small-scale power spectrum of cosmic density fluctuations through 21&nbsp;cm tomography prior to the epoch of structure formation
 |journal=[[Physical Review Letters]]
 |volume=92  |issue=21  |page=211301
 |arxiv=astro-ph/0312134  |s2cid=30510359
 |bibcode=2004PhRvL..92u1301L  |pmid=15245272
 |doi=10.1103/PhysRevLett.92.211301
 |url=https://cds.cern.ch/record/690135
 |via=[[CERN]]
}}
</ref>