Abstract
We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the Dyer-Roeder approximation does not correctly describe the effect of clumping. Instead, the redshift and the distance are determined by the average expansion rate, the matter density today and the null geodesic shear. In particular, the position of the CMB peaks is consistent with significant spatial curvature provided the expansion history is sufficiently close to the spatially flat LambdaCDM model.
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