# Inflation

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Inflation is a period of exponentially rapid expansion of the early universe.

An enormous number of models of inflation exist.[1] In most of them, a scalar field with a nonzero vacuum energy is the cause of the inflationary expansion.

## Inflation from Hubble Friction Edit this section

A simple example of inflation is provided by a scalar field with a harmonic oscillator potential. The expansion of the universe adds an effective friction term to the potential, causing the oscillations of the field around its minimum to become very slow. The field's energy density is effectively constant, causing the universe to expand exponentially for a significant period of time. (See e.g. section II of [2]).

## Inflation with a Shift Symmetry Edit this section

Another class of inflationary model is one where the inflaton potential is a periodic function, like a cosine. (cos(x) is said to have a shift symmetry because, if the value of x is shifted by a multiple of a wavelength, the value of cos(x) is unchanged.) Observations by the BICEP2 experiment (whose significance has since been cast into doubt) suggested that inflation occurred at energy scales that should have been affected by Planck-scale physics, and yet the spectrum of perturbations is simple, not exhibiting such effects. A fundamental shift symmetry could prevent additional Planck-scale interaction terms from being added to a simple inflaton potential. One example of such a model is Axion Monodromy Inflation.

## Starobinsky Inflation Edit this section

In Starobinsky inflation, which was the very first model of inflation, the exponential expansion is due to an addition $R^2$ term in the gravitational action. (It is therefore sometimes known as "$R^2$ inflation".) The observation by the Planck Collaboration, of a low scalar-to-tensor ratio in perturbations of the Cosmic Microwave Background, has recently made Starobinsky inflation popular among theorists.[3]

## ReferencesEdit this section

1. Martin, Jerome; Ringeval, Christophe., Vennin, Vincent.. "Encyclopedia Inflationaris". ArXiV.
2. Linde, Andrei. "Inflationary Theory versus Ekpyrotic/Cyclic Scenario". ArXiV.
3. Schreiber, Urs. nLab. http://ncatlab.org/nlab/show/Starobinsky+model+of+cosmic+inflation.