General Perturbations of Homogeneous and Orthogonal Locally Rotationally Symmetric Class II Cosmologies with Applications to Dissipative Fluids

TL;DR

This paper develops a comprehensive perturbation framework for LRS Class II cosmologies with a cosmological constant, including dissipative fluids, and explores vorticity generation from viscosity.

Contribution

It extends previous work by including general matter fields and dissipative effects within a covariant perturbation approach for LRS cosmologies.

Findings

Derives evolution equations for scalar, vector, tensor modes.

Reduces the system to closed subsystems in Eckart and causal theories.

Shows viscosity can generate vorticity in dissipative fluids.

Abstract

First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime. The perturbations, which are for a general energy-momentum tensor, include scalar, vector and tensor modes and extend some previous works where matter was assumed to be a perfect fluid. Through a harmonic decomposition, the system of equations is then transformed to evolution equations in time and algebraic constraints. This result is then applied to dissipative one-component fluids, and on using the simplified acausal Eckart theory the system is reduced to two closed subsystems governed by four and eight harmonic coefficients for the odd and even sectors respectively. The system is also seen to close in a simplified causal theory. It is then demonstrated, within the Eckart theory, how vorticity can be generated from viscosity.