Analyzing cosmological perturbations using the covariant approach

Abstract

This paper presents a complete set of equations using the covariant approach to the linear analysis of cosmological perturbations in general relativity without fixing gauges and by using gauge-invariant variables. In addition, Hawking's (1966) analysis of the evolution of vorticity and Jackson's analysis of the density evolution equation are extended to include the effects of an imperfect fluid in exact covariant form. The error in Hawking's covariant analysis is corrected, and the result is compared with other approaches using different gauges. In addition, the Ellis and Bruni (1989) equations are extended to the case of an imperfect fluid. An explicit solution for the evolution of large-scale cosmological density perturbations is presented, assuming a perfect fluid, but making no other restrictions on the background cosmological model.