Large-scale Perturbations from the Waterfall Field in Hybrid Inflation

TL;DR

This paper investigates how isocurvature fluctuations in the waterfall field during hybrid inflation contribute to large-scale curvature perturbations, revealing a peaked spectrum and extending the delta-N formalism to include these effects.

Contribution

It introduces an extension of the delta-N formalism to account for waterfall field fluctuations and estimates their impact on curvature perturbations in hybrid inflation.

Findings

Large-scale curvature perturbations from waterfall field are second-order.

The spectrum peaks around the Hubble horizon scale at inflation's end.

Perturbation amplitude on cosmological scales is approximately 10^{-54}.

Abstract

We estimate large-scale curvature perturbations from isocurvature fluctuations in the waterfall field during hybrid inflation, in addition to the usual inflaton field perturbations. The tachyonic instability at the end of inflation leads to an explosive growth of super-Hubble scale perturbations, but they retain the steep blue spectrum characteristic of vacuum fluctuations in a massive field during inflation. The power spectrum thus peaks around the Hubble-horizon scale at the end of inflation. We extend the usual delta-N formalism to include the essential role of these small fluctuations when estimating the large-scale curvature perturbation. The resulting curvature perturbation due to fluctuations in the waterfall field is second-order and the spectrum is expected to be of order 10^{-54} on cosmological scales.