Waterfall field in hybrid inflation and curvature perturbation

TL;DR

This paper analyzes the waterfall field's impact on curvature perturbations in hybrid inflation, revealing a highly non-Gaussian, blue-tilted spectrum with negligible large-scale effects but significant non-Gaussian features.

Contribution

It provides an analytical parameter dependence of the waterfall field's contribution and confirms the non-Gaussian nature of the curvature perturbation at the end of hybrid inflation.

Findings

Power spectrum is very blue with index 4, negligible on large scales.

Curvature perturbation is highly non-Gaussian, with a peak in the bispectrum at the equilateral limit.

The probability distribution function of the curvature perturbation is presented.

Abstract

We study carefully the contribution of the waterfall field to the curvature perturbation at the end of hybrid inflation. In particular we clarify the parameter dependence analytically under reasonable assumptions on the model parameters. After calculating the mode function of the waterfall field, we use the delta N formalism and confirm the previously obtained result that the power spectrum is very blue with the index 4 and is absolutely negligible on large scales. However, we also find that the resulting curvature perturbation is highly non-Gaussian and hence we calculate the bispectrum. We find that the bispectrum is at leading order independent of momentum and exhibits its peak at the equilateral limit, though it is unobservably small on large scales. We also present the one-point probability distribution function of the curvature perturbation.