Stochastic inflation with an extremely large number of e-folds

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7 Citations (Scopus)


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.

Original languageEnglish
Article number135097
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Publication statusPublished - 2020 Jan 10


  • Axion
  • Eternal inflation
  • IPMU19-0102
  • Stochastic inflation
  • TU-1090


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