ANALYZING COSMOLOGICAL PERTURBATIONS USING THE COVARIANT APPROACH

In this paper, we have presented 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, we have extended Hawking's analysis of the evolution of vorticity and Jackson's analysis of the density evolution equation to include the effects of an imperfect fluid in exact covariant form. We have explicitly corrected the error in Hawking's covariant analysis and compare the result with other approaches using different gauges. In addition, we have extended the recently derived Ellis and Bruni equations to the case of an imperfect fluid and show that their variables can be identified with the variables used by Bardeen in his gauge-invariant approach to cosmological perturbation analysis. Our calculation is done in the particle frame, so that the energy flux terms appear explicitly with a background that allows for a cosmological constant. Finally, we present an explicit solution for the evolution of large-scale cosmological density perturbations assuming a perfect fluid, but making no other restrictions on the background cosmological model. We conclude by emphasizing the advantages of the covariant approach in perturbation analysis and future applications of the covariant approach.