Perturbed Friedmann cosmologies filled with dust and radiation

Abstract

An infinite number of perturbed k=0 Friedmann cosmologies filled with dust and radiation is found. As we go up the sequence, the solutions contain an increasing number of integration functions. With the coordinate gauge adopted to co-move with the perturbed matter, the solution of a pair of coupled equations for the trace h of the metric perturbations and for the radiation density perturbations δρ_r is the key to the problem. An estimate is given of the temperature variation of the cosmic microwave background radiation due to the Sachs-Wolfe effect. It is found that the temperature fluctuations can grow faster than in the absence of radiation.