The spectrum of curvature perturbations from hybrid inflation

TL;DR

An exact expression for the amplitude of quantum fluctuations on all scales in the limit where the backreaction on the metric is neglected is given, a very good approximation for values of the inflaton field well below the Planck scale.

Abstract

We study the amplitude and spectral tilt of density perturbations in the simplest hybrid inflation models. We give an exact expression for the amplitude of quantum fluctuations on all scales in the limit where we can neglect the backreaction on the metric. This is a very good approximation for values of the inflaton field well below the Planck scale and our results remain valid far from the usual massless limit. We confirm that the primordial density spectrum in this model has a constant spectral index n>1 over all observable scales. For the small values of the tilt (n<1.4) required by observations, the results remain close to those obtained using the quasi-massless approximation.