# Contents

## 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.

More recent experiments (BICEP2) seem to favor the variant known as chaotic inflation.

## Variants

### 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 below at References – Higgs inflation.

### Axion inflation

field (physics)

standard model of particle physics

force field (physics) gauge bosons

scalar bosons

hadron (bound states of the above quarks)

minimally extended supersymmetric standard model

superpartner gauge field fermions

Exotica

## 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 (arXiv:1303.3787)

• Wikipedia, Inflation (cosmology)

### Original articles

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

### 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 (Match 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)

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

### 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

For a review and further pointers to the literature see

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