Does the isotropy of the CMB imply a homogeneous universe? Some generalized EGS theorems

We demonstrate that the high isotropy of the cosmic microwave background (C MB), combined with the Copernican principle, is not sufficient to prove hom ogeneity of the universe-in contrast to previous results on this subject. T he crucial additional factor not included in earlier work is the accelerati on of the fundamental observers. We find the complete class of irrotational perfect fluid spacetimes admitting an exactly isotropic radiation field fo r every fundamental observer and show that they are Friedmann-Lemaitre-Robe rtson-Walker (FLRW) if and only if the acceleration is zero. While inhomoge neous in general, these spacetimes all possess three-dimensional symmetry g roups, from which it follows that they also admit a thermodynamic interpret ation In addition to perfect fluids models we also consider multi-component fluid s containing noninteracting radiation, dust and a quintessential scalar fie ld or cosmological constant in which the radiation is isotropic for the geo desic (dust) observers, It is shown that the non-acceleration of the fundam ental observers forces these spacetimes to be FLRW. While it is plausible that fundamental observers (galaxies) in the real uni verse follow geodesics, it is strictly necessary to determine this from loc al observations for the cosmological principle to be more than an assumptio n. We discuss how observations may be used to test this.