Primordial Power Spectra from Anisotropic Inflation

TL;DR

This paper explores how coupling an Abelian gauge field to the inflaton during anisotropic inflation leads to direction-dependent primordial power spectra, affecting gravitational waves and curvature perturbations.

Contribution

It introduces a model of anisotropic inflation with persistent anisotropy and calculates its effects on primordial power spectra using the in-in formalism.

Findings

Primordial power spectra exhibit significant directional dependence.

Tensor power spectrum's anisotropy is suppressed relative to scalar spectrum.

Anisotropy can persist during inflation, violating Wald's no-hair theorem.

Abstract

We examine cosmological perturbations in a dynamical theory of inflation in which an Abelian gauge field couples directly to the inflaton, breaking conformal invariance. When the coupling between the gauge field and the inflaton takes a specific form, inflation becomes anisotropic and anisotropy can persist throughout inflation, avoiding Wald's no-hair theorem. After discussing scenarios in which anisotropy can persist during inflation, we calculate the dominant effects of a small persistent anisotropy on the primordial gravitational wave and curvature perturbation power spectra using the "in-in" formalism of perturbation theory. We find that the primordial power spectra of cosmological perturbations gain significant direction dependence and that the fractional direction dependence of the tensor power spectrum is suppressed in comparison to that of the scalar power spectrum.