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ΔN and the stochastic conveyor belt of ultra slow-roll inflation

Lookup NU author(s): Dr Gerasimos Rigopoulos



This is the authors' accepted manuscript of an article that has been published in its final definitive form by American Physical Society, 2021.

For re-use rights please refer to the publisher's terms and conditions.


© 2021 American Physical SocietyWe analyze field fluctuations during an ultra slow-roll phase in the stochastic picture of inflation and the resulting non-Gaussian curvature perturbation, fully including the gravitational backreaction of the field’s velocity. By working to leading order in a gradient expansion, we first demonstrate that consistency with the momentum constraint of general relativity prevents the field velocity from having a stochastic source, reflecting the existence of a single scalar dynamical degree of freedom on long wavelengths. We then focus on a completely level potential surface, , extending from a specified exit point , where slow roll resumes or inflation ends, to . We compute the probability distribution in the number of -folds required to reach , which allows for the computation of the curvature perturbation. We find that, if the field’s initial velocity is high enough, all points eventually exit through and a finite curvature perturbation is generated. On the contrary, if the initial velocity is low, some points enter an eternally inflating regime despite the existence of . In that case, the probability distribution for , although normalizable, does not possess finite moments, leading to a divergent curvature perturbation.

Publication metadata

Author(s): Prokopec T, Rigopoulos G

Publication type: Article

Publication status: Published

Journal: Physical Review D

Year: 2021

Volume: 104

Issue: 8

Online publication date: 01/10/2021

Acceptance date: 15/08/2021

Date deposited: 20/10/2021

ISSN (print): 2470-0010

ISSN (electronic): 2470-0029

Publisher: American Physical Society


DOI: 10.1103/PhysRevD.104.083505


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