A Green Function for Metric Perturbations due to Cosmological Density Fluctuations

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Abstract
We study scalar perturbations to a Robertson-Walker cosmological metric in terms of a pseudo-Newtonian potential, which emerges naturally from the solution of the field equations. This potential is given in terms of a Green function for matter density fluctuations of arbitrary amplitude whose time and spatial dependence are assumed known. The results obtained span both the linearized and Newtonian limits, and do not explicitly depend on any kind of averaging procedure, but make the valid assumption that the global expansion rate is that of a Friedmann-Robertson-Walker model. In addition, we discuss the similarity to diffusive processes in the evolution of the potential, and possible applications.

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