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Ultra-slow-roll inflation with quantum diffusion

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We consider the effect of quantum diffusion on the dynamics of the inflaton during a period of ultra-slow-roll inflation. We extend the stochastic-δΝ formalism to the ultra-slow-roll regime and show how this system can be solved analytically in both the classical-drift and quantum-diffusion dominated limits. By deriving the characteristic function, we are able to construct the full probability distribution function for the primordial density field. In the diffusion-dominated limit, we recover an exponential tail for the probability distribution, as found previously in slow-roll inflation. To complement these analytical techniques, we present numerical results found both by very large numbers of simulations of the Langevin equations, and through a new, more efficient approach based on iterative Volterra integrals. We illustrate these techniques with two examples of potentials that exhibit an ultra-slow-roll phase leading to the possible production of primordial black holes.
Original languageEnglish
Article number080
Pages (from-to)1-40
Number of pages40
JournalJournal of Cosmology and Astroparticle Physics
Issue number04
Publication statusPublished - 30 Apr 2021


  • 2101.05741

    Rights statement: This Accepted Manuscript is available for reuse under a CC BY-NC-ND licence after the 12 month embargo period provided that all the terms and conditions of the licence are adhered to.

    Accepted author manuscript (Post-print), 1.42 MB, PDF document

    Due to publisher’s copyright restrictions, this document is not freely available to download from this website until: 30/04/22

    Licence: CC BY-NC-ND

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