Generating the curvature perturbation at the end of inflation

TL;DR

This work investigates a mechanism by which a substantial portion of the primordial curvature perturbation $\zeta$ can be produced at the end of inflation. Using slow-roll, multi-field dynamics and the $\delta N$ formalism, the author derives general relations for the curvature spectrum, spectral tilt $n-1$, and non-Gaussianity parameters $f_{\rm NL}$ and $\tau_{\rm NL}$, and analyzes a sudden-end approximation to quantify the end-of-inflation contribution. A concrete hybrid-inflation model demonstrates how an end-surface dependent on a light field $\sigma$ can generate a non-negligible $\zeta_e$, with explicit expressions for $\phi_e'$ and $\phi_e''$ and conditions under which $\zeta_e$ dominates the total perturbation; the model yields predictions for $n-1$ and $f_{\rm NL}$ in terms of $\eta_{\sigma\sigma}$ and the end-surface derivatives. The results show that end-of-inflation perturbations are a natural and testable addition to standard inflaton-generated perturbations, potentially imprinting observable non-Gaussianity and tilt in the cosmic microwave background and large-scale structure.

Abstract

The dominant contribution to the primordial curvature perturbation may be generated at the end of inflation. Taking the end of inflation to be sudden, formulas are presented for the spectrum, spectral tilt and non-gaussianity. They are evaluated for a minimal extension of the original hybrid inflation model.