Stochastic inflation with an extremely large number of $e$-folds

TL;DR

This paper introduces a novel single-field slow-roll inflation model with a very large number of e-folds, achieved by adding a shallow local minimum near the potential's top, enabling extended inflation and consistent primordial perturbations.

Contribution

The model combines features of old and new inflation, allowing for extremely large e-folds through stochastic dynamics and subsequent slow-roll inflation.

Findings

Typical e-folds can reach as high as 10^{10^{10}}.

The scenario allows light scalars like the QCD axion to reach the Bunch-Davies distribution.

The model produces primordial density perturbations consistent with observations.

Abstract

We propose a class of single-field, slow-roll inflation models in which a typical number of $e$-folds can be extremely large. The key point is to introduce a very shallow local minimum near the top of the potential in a hilltop inflation model. In particular, a typical number of $e$-folds is enhanced if classical behavior dominates around the local minimum such that the inflaton probability distribution is drifted to the local minimum as a whole. After the inflaton escapes from the local minimum due to the stochastic dynamics, the ordinary slow-roll inflation follows and it can generate the primordial density perturbation consistent with observation. Interestingly, our scenario inherits the advantages of the old and new inflation: the typical $e$-folds can be extremely large as in the old inflation, and slow-roll inflation naturally follows after the stochastic regime as in the new inflation. In our numerical example, the typical number of $e$-folds can be as large as $10^{10^{10}}$, which is large enough for various light scalars such the QCD axion to reach the Bunch-Davies distribution.