The evolution of density perturbations in the universe

The evolution of energy density perturbations in the universe is investigated using the fluid flow approach proposed by Hawking (1966). The Bardeen equation for the comoving gage density perturbation is derived following the Lyth-Mukherjee (1988) approach, and the calculation is extended to the case of two uncoupled fluids, providing a derivation of the Kodama-Sasaki (1984, 1987) equation from which the evolution of separate density perturbations can be determined. An application of this approach to the cold dark matter scenarios is considered. It is shown that comoving and synchronous perturbations are related and that they become equal after matter domination and are related in a scale-independent way at early times.