# Multiple fields in stochastic inflation

## Abstract

Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δN formalism.

- Authors:

- Institute of Cosmology & Gravitation, University of Portsmouth,Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom)
- School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
- Department of Physics, University of Tehran,P.O. Box 14395-547, Tehran (Iran, Islamic Republic of)
- (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22572104

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2016; Journal Issue: 06; Other Information: PUBLISHER-ID: JCAP06(2016)043; OAI: oai:repo.scoap3.org:16161; cc-by Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COSMOLOGICAL INFLATION; COSMOLOGY; DIFFUSION EQUATIONS; INFLATIONARY UNIVERSE; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; PERTURBATION THEORY; POTENTIALS; QUANTUM GRAVITY; STOCHASTIC PROCESSES

### Citation Formats

```
Assadullahi, Hooshyar, Firouzjahi, Hassan, Noorbala, Mahdiyar, School of Astronomy, Institute for Research in Fundamental Sciences, Vennin, Vincent, and Wands, David.
```*Multiple fields in stochastic inflation*. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/06/043.

```
Assadullahi, Hooshyar, Firouzjahi, Hassan, Noorbala, Mahdiyar, School of Astronomy, Institute for Research in Fundamental Sciences, Vennin, Vincent, & Wands, David.
```*Multiple fields in stochastic inflation*. United States. doi:10.1088/1475-7516/2016/06/043.

```
Assadullahi, Hooshyar, Firouzjahi, Hassan, Noorbala, Mahdiyar, School of Astronomy, Institute for Research in Fundamental Sciences, Vennin, Vincent, and Wands, David. Fri .
"Multiple fields in stochastic inflation". United States.
doi:10.1088/1475-7516/2016/06/043.
```

```
@article{osti_22572104,
```

title = {Multiple fields in stochastic inflation},

author = {Assadullahi, Hooshyar and Firouzjahi, Hassan and Noorbala, Mahdiyar and School of Astronomy, Institute for Research in Fundamental Sciences and Vennin, Vincent and Wands, David},

abstractNote = {Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δN formalism.},

doi = {10.1088/1475-7516/2016/06/043},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 06,

volume = 2016,

place = {United States},

year = {Fri Jun 24 00:00:00 EDT 2016},

month = {Fri Jun 24 00:00:00 EDT 2016}

}