PROVING ALMOST-HOMOGENEITY OF THE UNIVERSE - AN ALMOST EHLERS-GEREN-SACHS THEOREM

We show that if all fundamental observers measure the cosmic microwave background radiation to be almost isotropic in an expanding universe region, then that universe is locally almost spatially homogeneous and isotropic in that region. This shows the stability of the important e xact result of this type previously proved by Ehlers, Geren, and Sachs , and formalizes the way in which almost-isotropy of the background ra diation gives evidence that the universe is almost a Friedmann-Lemaitr e-Robertson-Walker (FLRW) spacetime. This is the needed foundation for all the recent analyses, based on the Sachs-Wolfe effect, of how back ground radiation anisotropies relate to growing density inhomogeheitie s in an almost-FLRW expanding universe.