Geocentrism reexamined

Observations show that the universe is nearly isotropic on very large scales. It is much more difficult to show that the universe is radially homogeneous, that is, independent of the distance from us, or, equivalently, that the universe is isotropic about distant points. This is usually taken as an axiom, since otherwise we would occupy a special position. Here we consider several empirical arguments for radial homogeneity, all of them based on the cosmic microwave background (CMB). We assume that physical laws are uniform, but we suppose that structure on very large scales may not be. The tightest limits for inhomogeneity on the scale of the horizon appear to be of the order of ten percent. These involve observations of the Sunyaev-Zel'dovich effect in clusters of galaxies, excitation of low-energy atomic transitions, and the accurate thermal spectrum of the CMB. Weaker limits from primordial nucleosynthesis are discussed briefly.