The Nature of Primordial Fluctuations from Anisotropic Inflation

TL;DR

This paper investigates the statistical properties of primordial fluctuations in anisotropic inflation, revealing dominant anisotropic couplings, enhanced statistical anisotropy in curvature perturbations, and novel correlations and polarization effects.

Contribution

It introduces the canonical gauge for anisotropic inflation, analyzes the coupling structures, and uncovers new anisotropic effects and correlations not present in isotropic models.

Findings

Dominant anisotropic coupling among variables.

Enhanced statistical anisotropy in curvature perturbations.

Presence of cross correlations and linear polarization of gravitational waves.

Abstract

We study the statistical nature of primordial fluctuations from an anisotropic inflation which is realized by a vector field coupled to an inflaton. We find a suitable gauge, which we call the canonical gauge, for anisotropic inflation by generalizing the flat slicing gauge in conventional isotropic inflation. Using the canonical gauge, we reveal the structure of the couplings between curvature perturbations, vector waves, and gravitational waves. We identify two sources of anisotropy, i.e. the anisotropy due to the anisotropic expansion of the universe and that due to the anisotropic couplings among variables. It turns out that the latter effect is dominant. Since the coupling between the curvature perturbations and vector waves is the strongest one, the statistical anisotropy in the curvature perturbations is larger than that in gravitational waves. We find the cross correlation between the curvature perturbations and gravitational waves which never occurs in conventional inflation. We also find the linear polarization of gravitational waves. Finally, we discuss cosmological implication of our results.