# Inflation in random Gaussian landscapes

## Abstract

We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.

- Authors:

- Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

- Publication Date:

- OSTI Identifier:
- 22676188

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 05; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BROWNIAN MOVEMENT; COMPUTERIZED SIMULATION; CORRELATION FUNCTIONS; CORRELATIONS; DENSITY; DISTRIBUTION; FLUCTUATIONS; INFLATIONARY UNIVERSE; ONE-DIMENSIONAL CALCULATIONS; PROBABILITY; RANDOMNESS

### Citation Formats

```
Masoumi, Ali, Vilenkin, Alexander, and Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu.
```*Inflation in random Gaussian landscapes*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/05/053.

```
Masoumi, Ali, Vilenkin, Alexander, & Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu.
```*Inflation in random Gaussian landscapes*. United States. doi:10.1088/1475-7516/2017/05/053.

```
Masoumi, Ali, Vilenkin, Alexander, and Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu. Mon .
"Inflation in random Gaussian landscapes". United States.
doi:10.1088/1475-7516/2017/05/053.
```

```
@article{osti_22676188,
```

title = {Inflation in random Gaussian landscapes},

author = {Masoumi, Ali and Vilenkin, Alexander and Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu},

abstractNote = {We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.},

doi = {10.1088/1475-7516/2017/05/053},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 05,

volume = 2017,

place = {United States},

year = {Mon May 01 00:00:00 EDT 2017},

month = {Mon May 01 00:00:00 EDT 2017}

}