Theory of cosmological perturbations in an anisotropic universe

TL;DR

This paper develops a comprehensive theory of cosmological perturbations in an anisotropic Bianchi I universe, identifying gauge-invariant variables, their physical degrees of freedom, and implications for primordial anisotropy effects on cosmic microwave background anomalies.

Contribution

It generalizes the Mukhanov-Sasaki variables to anisotropic backgrounds, derives the second-order action, and explores the impact of anisotropy on primordial perturbations and their observational signatures.

Findings

Identification of gauge-invariant variables in anisotropic universe

Derivation of second-order action for perturbations

Prediction of anisotropy-induced effects on CMB anomalies

Abstract

This article describes the theory of cosmological perturbations around a homogeneous and anisotropic universe of the Bianchi I type. Starting from a general parameterisation of the perturbed spacetime a la Bardeen, a complete set of gauge invariant variables is constructed. Three physical degrees of freedom are identified and it is shown that, in the case where matter is described by a scalar field, they generalize the Mukhanov-Sasaki variables. In order to show that they are canonical variables, the action for the cosmological perturbations at second order is derived. Two major physical imprints of the primordial anisotropy are identified: (1) a scalar-tensor ``see-saw'' mechanism arising from the fact that scalar, vector and tensor modes do not decouple and (2) an explicit dependence of the statistical properties of the density perturbations and gravity waves on the wave-vector instead of its norm. This analysis extends, but also sheds some light on, the quantization procedure that was developed under the assumption of a Friedmann-Lemaitre background spacetime, and allows to investigate the robustness of the predictions of the standard inflationary scenario with respect to the hypothesis on the symmetries of the background spacetime. These effects of a primordial anisotropy may be related to some anomalies of the cosmic microwave background anisotropies on large angular scales.