Inflation in random Gaussian landscapes

TL;DR

This paper introduces new analytic and numerical methods to study the statistical properties of slow-roll inflation in random Gaussian landscapes, providing universal distributions for key inflationary parameters.

Contribution

It develops techniques that avoid inconsistencies of previous methods, enabling analysis of small-field inflation and potential extensions to multi-field and large-field models.

Findings

Universal probability distributions for the number of e-folds and spectral index parameters.

Methods applicable to both small-field and large-field inflation scenarios.

Avoidance of potential issues present in earlier Brownian motion approaches.

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 $n_s$ and its running $\alpha_s$. 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.