Cosmological Perturbations and the Weyl Tensor

Abstract

In a previous work the authors have solved the Einstein equations of General Relativity for a class of metrics with constant spatial curvature where it was found a non vanishing Weyl tensor due to the presence of an anisotropic pressure component associated to a primordial magnetic field. Here, we perform the perturbative analysis of this model in order to study the gravitational stability under linear scalar perturbations. For this purpose, we take the Quasi-Maxwellian formalism of General Relativity as our framework, which o˙ers a naturally covariant and gauge-invariant approach to deal with perturbations that are directly linked to observational quantities. We also consider a generalization of the causal thermodynamics to include the e˙ect of the non-null Weyl tensor by introducing a new “viscosity” term.