Finslerian perturbation for the $\Lambda$CDM model

TL;DR

This paper introduces a Finslerian perturbation to the $mbda$CDM model, breaking isotropy and modifying the primordial gravitational wave spectrum, especially on sub-horizon scales.

Contribution

It develops a Finslerian framework for cosmological perturbations, deriving modified geodesic and gravitational field equations within Randers-Finsler spacetime.

Findings

Primordial power spectrum remains unchanged for super-horizon perturbations.

Power spectrum is modified for sub-horizon perturbations.

Finslerian perturbation breaks isotropic symmetry even without scalar perturbations.

Abstract

We present Finslerian perturbation for the $\Lambda$CDM model, which breaks the isotropic symmetry of the universe. The analysis on the Killing vectors shows that the Randers-Finsler spacetime breaks the isotropic symmetry even if the scalar perturbations of the FRW metric vanish. In Randers-Finsler spacetime, the modified geodesic equation deduces a modified Boltzmann equation. We propose a perturbational version of the gravitational field equation in Randers-Finsler spacetime, where we have omitted the curvature tensor that does not belong to the base space of the tangent bundle. The gravitational field equations for the gravitational wave are also presented. The primordial power spectrum of the gravitational wave is investigated. We show that the primordial power spectrum for super-horizon perturbations is unchanged. For sub-horizon perturbations, however, the power spectrum is modified.