Space-Dependent Step Features: Transient Breakdown of Slow-roll, Homogeneity and Isotropy During Inflation

TL;DR

This paper explores how space-dependent step features in the inflaton potential can cause transient breakdowns of slow-roll inflation, leading to potential primordial anisotropies and modifications in curvature perturbations.

Contribution

It generalizes the step feature to include space dependence, analyzing its effects on curvature perturbations and primordial anisotropy during inflation.

Findings

Small inhomogeneities have minimal impact on the quantum power spectrum.

Large inhomogeneities can dominate curvature perturbations, introducing anisotropy.

Resonance effects from mode coupling are present but minor.

Abstract

A step feature in the inflaton potential can model a transient breakdown of slow-roll inflation. Here we generalize the step feature to include space-dependence, allowing it also to model a breakdown of homogeneity and isotropy. The space-dependent inflaton potential generates a classical curvature perturbation mode characterized by the wavenumber of the step inhomogeneity. For inhomogeneities small compared with the horizon at the step, space-dependence has a small effect on the curvature perturbation. Therefore the smoothly oscillating quantum power spectrum predicted by the homogeneous step is robust with respect to sub-horizon space-dependence. For inhomogeneities equal to or greater than the horizon at the step, the space-dependent classical mode can dominate, producing a curvature perturbation in which modes of wavenumber determined by the step inhomogeneity are superimposed on the oscillating power spectrum. Generation of a space-dependent step feature may therefore provide a mechanism to introduce primordial anisotropy into the curvature perturbation. Space-dependence also modifies the quantum fluctuations, in particular via resonance-like features coming from mode coupling to amplified superhorizon modes. However these effects are small relative to the classical modes.