Recursive Stochastic Effects in Valley Hybrid Inflation

TL;DR

This paper applies a recursive stochastic formalism to analyze hybrid inflation, revealing how stochastic effects influence the waterfall phase duration and the spectral tilt of curvature perturbations, with implications for inflationary models.

Contribution

It introduces a recursive approach to compute stochastic effects in hybrid inflation, highlighting the impact on waterfall dynamics and perturbation spectra.

Findings

Stochastic effects increase the waterfall phase duration.

Quasi-stationarity breaks down in short-lived waterfalls.

Stochastic effects worsen the blue tilt of curvature perturbations.

Abstract

Hybrid Inflation is a two-field model where inflation ends by a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in Ref. [1], these effects are consistently computed. Through an analysis of back-reaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that quasi-stationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. It is found that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, it is found that stochastic effects worsen the blue tilt of the curvature perturbations by an order one factor when compared with the usual slow-roll contribution.