۱- Introduction

۲- Stochastic inflation with large N

۳- Example model

۴- Discussion and conclusions

References

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 101010 , which is large enough for various light scalars such the QCD axion to reach the Bunch-Davies distribution.

Introduction

How long can inflation last? From the observational point of view, the total number of e-folds, N, must be larger than ∼ ۵۰–۶۰, which weakly depends on the inflation scale and thermal history after inflation. On the other hand, an extremely long duration of inflation is often required in certain scenarios. For instance, the relaxation model [1], the stochastic axion scenario [2–۵], a quintessence model [6,7] demand the e-folding number of log10 N ∼ O(10), depending on model parameters.1 The purpose of this Letter is to provide a simple single-field, slow-roll inflation model whose typical number of e-folds is extremely large. There is a variety of inflation models which last very long. In the string/axion landscape [10–۱۷], there are many local minima where the old inflation takes place and continues until the inflaton tunnels toward one of the adjacent local minima with a lower energy through bubble formation. In this case, the typical e-folding number can be exponentially large. However, one needs slow-roll inflation after the bubble formation to explain the observed cosmic microwave background (CMB) temperature/polarization anisotropies. For this, one may need another light scalar, in which case the two inflation scales are not related to each other, in general.