Observational homogeneity of the Universe

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Abstract
A new approach to observational homogeneity is presented. The observation that stars and galaxies in distant regions appear similar to those nearby may be taken to imply that matter has had a similar thermodynamic history in widely separated parts of the Universe (the Postulate of Uniform Thermal Histories, or PUTH). Let us now suppose that similar thermodynamic histories imply similar dynamical histories. Then the distant apparent similarity is evidence for spatial homogeneity of the Universe. Using General Relativity to test this idea we take a perfect fluid model and implement PUTH by the condition that the density and entropy per baryon shall be the same function of the proper time along all galaxy world-lines. The standard models of cosmology, the Bianchi models, and the Kantowski–Sachs models all satisfy this condition, and are all spatially homogeneous. We now ask whether this condition ensures spatial homogeneity in general. Somewhat to our surprise, we find examples which show that it does not.

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