Obtaining the metric of our Universe

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Abstract
We formulate a method for solving the gravitational field equations for perturbations to a Friedmann-Robertson-Walker metric, which does not depend on any kind of averaging procedure or make any a priori assumptions about the magnitude of fluctuations in the matter variables. We present a Green function for obtaining the effective potential which characterizes the metric perturbations directly from the (possibly large) density fluctuations, and describe the application to astrophysical observations, for example, the angular-diameter distance-versus-redshift relation. The results do not assume a particular model for the formation of structure in the matter distribution, and are valid everywhere in our Universe outside of strong-field regions (e.g., black holes).