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An analytical model of a void, at an intermediate epoch between recombination and the present, is studied, and its gravitational influence on photons passing through it is considered. The background universe is a flat Friedmann-Robertson-Walker cosmology with dust. The deviation of redshift for the photons as a function of impact parameter is calculated to lowest order. This is used to approximate the cosmic background radiation anisotropy expected of a universe filled with such voids. The temperature fluctuation with voids the size of that in Bootes is of the order 10 to the -6th. This is about two orders of magnitude lower than present published limits.
Thompson et al. (Sun,) studied this question.