An analytic approach to perturbations from an initially anisotropic universe

TL;DR

This paper analytically derives the spectra of cosmological perturbations from an initially anisotropic universe, revealing polarization asymmetries in gravitational waves during the isotropization process.

Contribution

It provides explicit analytic forms for perturbation spectra in anisotropic backgrounds using WKB approximations, extending previous work on anisotropic cosmologies.

Findings

High momentum modes follow WKB approximation during isotropization.

Planar modes are amplified during anisotropic expansion.

Gravitational wave spectra exhibit polarization asymmetry due to initial mode mixing.

Abstract

We present the analytic forms for the spectra of the cosmological perturbations from an initially anisotropic universe for the high momentum modes in the context of WKB approximations, as the continuation of the work [29]. We consider the Einstein gravity coupled to a light scalar field. We then assume that the scalar field has the zero velocity initially and then slowly rolls down on the potential toward the origin. In the slow-roll approximations, the Kasner-de Sitter universe with a planar symmetry is a good approximation as the background evolution. Quantization of the perturbations in the adiabatic vacuum, which we call the anisotropic vacuum, is carried out. For non-planar high momentum modes whose comoving momentum component orthogonal to the plane is bigger than the Hubble parameter at the inflationary phase, the WKB approximation is valid for the whole stage of the isotropization. On the other hand, the planar modes whose comoving momentum component orthogonal to the plane is comparable to the Hubble parameter, is amplified during the process of the anisotropic expansion. In the final gravitational wave spectra, we find that there is an asymmetry between the two polarizations of the gravitational wave because the initial mode mixing does not vanish.