Dissipative Perturbations on LRS Class II Cosmologies Using the 1+1+2 Covariant Split of Spacetime

Sammanfattning: By including dissipative fluxes in the description, this thesis extends previous results regarding first order perturbations on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II cosmologies using the 1 + 1 + 2 covariant split of spacetime. Whereas previous works consider perturbations of perfect fluid type, perturbations pertaining to heat flux and fluid viscosity are here studied with the aim to ascertain their effect on the evolution of the fluid vorticity. The studied perturbations include scalar, vector, and tensor modes, and are harmonically decomposed to yield a system of ordinary differential equations. These equations, originating from the Bianchi identities, the Ricci identities for certain preferred vector fields, and the thermodynamic Eckart theory, then decouple into two independent systems. These separately closed systems, with four and eight remaining variables respectively, describe the evolution of perturbations pertaining to the Weyl tensor and the fluid shear, vorticity, heat flow, energy density, and number density. From the final system of equations it is seen that the inclusion of heat flux and fluid viscosity has the possibility to yield mechanisms for generating vorticity, even if this vorticity vanishes initially. This is in contrast to the case of barotropic perfect fluids, for which it can be shown that vorticity perturbations cannot be generated. The validity of the results presented here can be questioned, as the Eckart theory, which violates causality, is employed to describe the detailed thermodynamic properties of the fluid. However, on time scales much larger than the relaxation times of the fluid, it should still provide a decent description of the dissipative phenomena, provided that certain couplings between the dissipative fluxes can be neglected.