nLab cosmic inflation

Idea

In the context of cosmology, cosmic inflation is a model (in theoretical physics) that can explain certain large-scale features of the observable universe (flatness, horizon problem, CMB anisotropy) by assuming a finite period of drastic expansion of the universe shortly after the big bang. Cosmic inflation is part of the standard model of cosmology.

The typical model of cosmic inflation adds to a standard FRW model simply a scalar field $\phi$ – then called the inflaton field – with standard kinetic term and some potential term. If the potential term is chosen suitably one can obtain solutions to Einstein's equations of this simple homogenous and isotropic model which exhibit “slow roll behaviour” for $\phi$, meaning that $\phi$ (homogeneous in space) starts out in the vicinity of the big bang with some finite value and then slowly “rolls down” its potential well (where one speaks in the analogy with the model describing a single particle on the real line in the given potential, which has the same kind of action functional). Therefore in this “slow roll” period the contribution of $\phi$ to the FRW model is essentially that of a cosmological constant and so this drives the expansion of the “universe” in this model. But since $\phi$ is only approximately constant it eventually reaches the minimum of its potential well. Again, if the potential parameters of the model are chosen suitably one can arrange that it stays there (called the “graceful exit property” of the inflationary model) and so it stops driving the expansion of the “universe”. In conclusion this yields variants of the FRW model that exhibit pronounced expansion shortly after the initial singularity and then asymptote to the behaviour of the plain FRW model. This is what is called cosmic inflation.

Simple as it is, this model has proven to successfully match the observations that it was designed to match (the large-scale homogeneity of the observable universe, notably). But of course people are trying all kinds of variants, too. A central conceptual problem of most of these models is that it is unclear what the field $\phi$ should be in terms of particle physics or other known phyisics. In some variants it is identified with the Higgs field, in other it is a scalar moduli field of some Kaluza-Klein compactification, but all of this is speculative.

The experimental data (PlanckCollaboration 13, BICEP-Keck-Planck 15, PlanckCollaboration 15) strongly favors the Starobinsky model of cosmic inflation.

Variants

Old inflation

(Guth 91, Sato 81)

New inflation

(Linde 82, Albrecht-Steinhardt 82)

Eternal inflation

• eternal inflation

Chaotic inflation

chaotic inflation

(Linde 83)

Candidates for the inflaton field

Higgs inflation

The idea that the inflaton field in cosmology might be the Higgs field from the standard model of particle physics is as old as the idea of inflation itself, but at least in the naive versions it seems to be ruled out by data. However, with the experimental detection of the previously hypothesized Higgs field itself, the topic is gaining interest again and various variations are being proposed to solve the problems with the naive idea, for instance a small non-minimal coupling of the Higgs field to gravity (see e.g. Atkins 12, Kamada 12, Kehagias 12).

In particular, the near-criticality of the Higgs potential (see there) has been argued to be just the right condition to make Higgs inflation viable (Jegerlehner 13, Jegerlehner 14, Jegerlehner 15, Jegerlehner 18), for review see also Rubio 18.

Axion inflation

see axion inflation

Higher curvature inflation (Starobinsky model)

It is possible that instead of the inflaton being a fundamental scalar field, it is an effective result of higher curvature corrections to gravity.

The first such $R^2$ correction leads to the Starobinsky model of cosmic inflation, which sits right in the middle of the parameter space preferred by the PLANCK satellite data.

Discussion of inflationary effects of ever higher curvature corrections includes Arciniega-Edelstein-Jaime 18, ABCEHJ 18.

Ekpyrotic cosmology

See ekpyrotic cosmology.

Related concepts

• eternal cosmic inflation

• cosmology

• FRW model

• big bang, steady state model

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

• photon - electromagnetic field (abelian Yang-Mills field)

• W, Z, B-boson - electroweak field (Yang-Mills field)

• gluon - strong nuclear force (Yang-Mills field)

• graviton - field of gravity

• infraparticle

scalar bosons

• Higgs boson, inflaton (scalar field)

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the standard model of particle physics:
generation of fermions	1st generation	2nd generation	3d generation
quarks ($q$)
up-type	up quark ($u$)	charm quark ($c$)	top quark ($t$)
down-type	down quark ($d$)	strange quark ($s$)	bottom quark ($b$)
leptons
charged	electron	muon	tauon
neutral	electron neutrino	muon neutrino	tau neutrino
bound states:
mesons	light mesons: pion ($u d$) ρ-meson ($u d$) ω-meson ($u d$) f1-meson a1-meson	strange-mesons: ϕ-meson ($s \bar s$), kaon, K*-meson ($u s$, $d s$) eta-meson ($u u + d d + s s$) charmed heavy mesons: D-meson ($u c$, $d c$, $s c$) J/ψ-meson ($c \bar c$)	bottom heavy mesons: B-meson ($q b$) ϒ-meson ($b \bar b$)
baryons	nucleons: proton $(u u d)$ neutron $(u d d)$

(also: antiparticles)

effective particles

• Goldstone bosons

hadrons (bound states of the above quarks)

• meson

  • scalar meson

    • σ-meson

    • pion

    • kaon

    • D-meson

    • B-meson

  • vector meson

    • ω-meson

    • ρ-meson

    • f1-meson

    • a1-meson

    • b1-meson

    • h1-meson

    • K*-meson

  • tensor meson

  • quarkonium

    • charmonium

    • ϒ-meson

• exotic meson

  • XYZ meson

  • tetraquark

• baryon

  • nucleon

    • proton

    • neutron

    • chemical element

      • carbon

      • nitrogen

  • Lambda baryon

  • pentaquark

solitons

• Skyrmion

• caloron

• instanton

in grand unified theory

• leptoquark

• Z'-boson

minimally extended supersymmetric standard model

superpartners

bosinos:

• gravitino - field of supergravity (Rarita-Schwinger field)

• gaugino - super Yang-Mills field

• gluino

sfermions:

• squark

dark matter candidates

• WIMP

• axion

Exotica

• preon

• graviphoton

• dilaton

• monopole

• dual graviton

• giant graviton

auxiliary fields

• ghost field

• antifield

• antighost field, Nakanishi-Lautrup field

References

Reviews

• Andrei Linde, Particle Physics and Inflationary Cosmology, Harwood, Chur (1990).

• A. R. Liddle, D. H. Lyth, Cosmological inflation and large-scale structure, Cambridge University Press (2000).

• Shinji Tsujikawa, Introductory review of cosmic inflation, lecture notes given at The Second Tah Poe School on Cosmology Modern Cosmology, Naresuan (2003) (arXiv:hep-ph/0304257).

• Jerome Martin, Christophe Ringeval, Vincent Vennin, Encyclopaedia Inflationaris, Phys. Dark Univ. 5-6 (2014) 75-235 [arXiv:1303.3787, doi:10.1016/j.dark.2014.01.003]

• Jerome Martin, The Theory of Inflation (arXiv:1807.11075)

• Debika Chowdhury, Jerome Martin, Christophe Ringeval, Vincent Vennin, Inflation after Planck: Judgment Day (arXiv:1902.03951)

With emphasis on the Schwinger effect:

• Jerome Martin, Inflationary Perturbations: the Cosmological Schwinger Effect, Lect. Notes Phys. 738:193-241, 2008 (arXiv:0704.3540, doi:10.1007/978-3-540-74353-8_6)

See also:

• Wikipedia, Inflation (cosmology)

Original articles

• Demosthenes Kazanas, Dynamics of the universe and spontaneous symmetry breaking, Astrophysical Journal, Part 2 - Letters to the Editor, 241 (Oct. 15, 1980) L59-L63 [doi:10.1086/183361]

• Aleksei Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 (1980) 99-102 [doi:10.1016/0370-2693(80)90670-X]

  (cf. Starobinsky model of cosmic inflation)

• Alan Guth, Phys. Rev. D 23, 347 (1981).

• K. Sato, Mon. Not. R. Astron. Soc. 195, 467 (1981); Phys. Lett. 99B, 66 (1981)

• Andrei Linde, Phys. Lett. 108B, 389 (1982)

• A. Albrecht and Paul Steinhardt, Phys. Rev. Lett. 48, 1220 (1982)

• Andrei Linde, Phys. Lett. 129B, 177 (1983).

On structure formation during inflation by inhomogeneous quantum cosmology:

• Martin Bojowald, Ding Ding, Canonical description of cosmological backreaction, JCAP 03 (2021) 083

  (arXiv:2011.03018)

In supersymmetric quantum cosmology:

• N.E. Martínez-Pérez, C. Ramírez, V.M. Vázquez Báez, Phenomenological inflationary model in Supersymmetric Quantum Cosmology [arXiv:2208.04412]

Experimental evidence

• C. L. Bennett et al. First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results, Astrophys.J.Suppl.148:1 (2003) (arXiv:astro-ph/0302207)

• H .V. Peiris et al, First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation, Astrophys.J.Suppl.148:213,2003 (arXiv:astro-ph/0302225)

• Planck Collaboration, Planck 2013 results. XXII. Constraints on inflation (arXiv:1303.5082)

  • Resonaances, Planck about inflation

  • Andrei Linde, Inflationary Cosmology after Planck 2013 (arXiv:1402.0526)

• A Joint Analysis of BICEP2/Keck Array and Planck Data (arXiv:1502.00612)

• Planck Collaboration, Planck 2015, Overview of results (pdf)

• Debika Chowdhury, Jerome Martin, Christophe Ringeval, Vincent Vennin, Inflation after Planck: Judgment Day (arxiv:1902.03951)

Inflation from higher curvature corrections

Besides the references at Starobinsky model of cosmic inflation the following discuss inflation driven by higher curvature corrections:

• Gustavo Arciniega, Jose D. Edelstein, Luisa G. Jaime, Towards purely geometric inflation and late time acceleration (arXiv:1810.08166)

• Gustavo Arciniega, Pablo Bueno, Pablo A. Cano, Jose D. Edelstein, Robie A. Hennigar, Luisa G. Jaimem, Geometric Inflation (arXiv:1812.11187)

Higgs field inflation

Literature discussing whether or how the Higgs field might be identified as the inflaton field includes

• Michael Atkins, Could the Higgs boson be the inflaton?, talk (March 2012) (pdf)

• Kohei Kamada, Generalized Higgs inflation models, talk at PLANCK 2012 (May 2012)(pdf)

• Alex Kehagias, New Higgs inflation, talk (September 2012) (pdf)

• Takehiro Nabeshima, A model for Higgs inflation and its testability at the ILC, talk (October 2012) (pdf)

• Javier Rubio, Higgs inflation, Front. Astron. Space Sci. 5:50 (2019) (arXiv:1807.02376)

A popular account in the context of the 2013 Plack Collaboration results is in

• Matthew Strassler, Cosmic Conflation: The Higgs, The Inflaton, and Spin

Discussion of Higgs inflation with emphasis on relation to the near-criticality of the Higgs field:

• Fred Jegerlehner, The hierarchy problem of the electroweak Standard Model revisited (arXiv:1305.6652)

• Fred Jegerlehner, Higgs inflation and the cosmological constant, Acta Phys.Polon. B45 (2014) 1215-1254 (arXiv:1402.3738)

• Fred Jegerlehner, About the role of the Higgs boson in the evolution of the early universe (arXiv:1406.3658)

• Fred Jegerlehner, The hierarchy problem and the cosmological constant problem in the Standard Model (arXiv:1503.00809)

• Fred Jegerlehner, The Hierarchy Problem and the Cosmological Constant Problem Revisited – A new view on the SM of particle physics (arXiv:1812.03863)

See also

• Tommi Tenkanen, Eemeli Tomberg, Initial conditions for plateau inflation (arXiv:2002.02420)

Gauge field inflation

Literature discussing whether or how gauge field might be identified as the inflaton field include

• A. Maleknejad, M. M. Sheikh-Jabbari, J. Soda, Gauge Fields and Inflation (arXiv:1212.2921)

String modeled inflation

In string theory the inflaton field can be modeled by various effects, such as

• open string stretching between D-brane-anti D-brane pairs.

For review and further pointers to the literature see

• Cliff Burgess, M. Cicoli, F. Quevedo, String Inflation After Planck 2013 (arXiv:1306.3512)

• Daniel Baumann, Liam McAllister, Inflation and String Theory, Cambridge University Press (2015) [arXiv:1404.2601, doi:10.1017/CBO9781316105733]

See also at string phenomenology.