Horizon crossing and inflation with large \eta

TL;DR

This paper investigates the validity of the horizon crossing formalism in inflation, derives a general relation for its applicability, and explores models with large ta that challenge conventional assumptions, potentially enabling new inflationary models.

Contribution

It derives a general relation for horizon crossing formalism validity and analyzes models with large ta that can produce scale-invariant spectra despite rapid superhorizon evolution.

Findings

The horizon crossing formalism is valid under specific conditions.

Models with ta=3 can produce scale-invariant spectra.

Large ta solutions may avoid the ta problem in supergravity.

Abstract

I examine the standard formalism of calculating curvature perturbations in inflation at horizon crossing, and derive a general relation which must be satisfied for the horizon crossing formalism to be valid. This relation is satisfied for the usual cases of power-law and slow roll inflation. I then consider a model for which the relation is strongly violated, and the curvature perturbation evolves rapidly on superhorizon scales. This model has Hubble slow roll parameter $\eta = 3$, but predicts a scale-invariant spectrum of density perturbations. I consider the case of hybrid inflation with large $\eta$, and show that such solutions do not solve the ``$\eta$ problem'' in supergravity. These solutions correspond to field evolution which has not yet relaxed to the inflationary attractor solution, and may make possible new, more natural models on the string landscape.