# Solving stochastic inflation for arbitrary potentials

## Abstract

A perturbative method for solving the Langevin equation of inflationary cosmology in the presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the inflaton field for an arbitrary potential, with or without the volume effects taken into account. The perturbative method is then applied to various concrete models, namely, large field, small field, hybrid, and running mass inflation. New results on the stochastic behavior of the inflaton field in those models are obtained. In particular, it is confirmed that the stochastic effects can be important in new inflation while it is demonstrated they are negligible in (vacuum dominated) hybrid inflation. The case of stochastic running mass inflation is discussed in some details and it is argued that quantum effects blur the distinction between the four classical versions of this model. It is also shown that the self-reproducing regime is likely to be important in this case.

- Authors:

- Institut d'Astrophysique de Paris, GReCO, UMR 7095-CNRS, Universite Pierre et Marie Curie, 98bis Boulevard Arago, 75014 Paris (France)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20776733

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.043516; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; APPROXIMATIONS; COSMOLOGY; DISTRIBUTION; INFLATIONARY UNIVERSE; LANGEVIN EQUATION; MASS; POTENTIALS; PROBABILITY; STOCHASTIC PROCESSES

### Citation Formats

```
Martin, Jerome, Musso, Marcello, and Department of Physics-Theory Group, University of Texas at Austin, 1 University Station C1608, Austin, Texas 78712-0269 USA.
```*Solving stochastic inflation for arbitrary potentials*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.043516.

```
Martin, Jerome, Musso, Marcello, & Department of Physics-Theory Group, University of Texas at Austin, 1 University Station C1608, Austin, Texas 78712-0269 USA.
```*Solving stochastic inflation for arbitrary potentials*. United States. doi:10.1103/PhysRevD.73.043516.

```
Martin, Jerome, Musso, Marcello, and Department of Physics-Theory Group, University of Texas at Austin, 1 University Station C1608, Austin, Texas 78712-0269 USA. Wed .
"Solving stochastic inflation for arbitrary potentials". United States.
doi:10.1103/PhysRevD.73.043516.
```

```
@article{osti_20776733,
```

title = {Solving stochastic inflation for arbitrary potentials},

author = {Martin, Jerome and Musso, Marcello and Department of Physics-Theory Group, University of Texas at Austin, 1 University Station C1608, Austin, Texas 78712-0269 USA},

abstractNote = {A perturbative method for solving the Langevin equation of inflationary cosmology in the presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the inflaton field for an arbitrary potential, with or without the volume effects taken into account. The perturbative method is then applied to various concrete models, namely, large field, small field, hybrid, and running mass inflation. New results on the stochastic behavior of the inflaton field in those models are obtained. In particular, it is confirmed that the stochastic effects can be important in new inflation while it is demonstrated they are negligible in (vacuum dominated) hybrid inflation. The case of stochastic running mass inflation is discussed in some details and it is argued that quantum effects blur the distinction between the four classical versions of this model. It is also shown that the self-reproducing regime is likely to be important in this case.},

doi = {10.1103/PhysRevD.73.043516},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}