Ehlers–Geren–Sachs theorem

Using the fact that, as measured from Earth, the cosmic microwave background is indeed highly isotropic—the temperature characterizing this thermal radiation varies only by tenth of thousandth of a kelvin with the direction of observations—and making the Copernican assumption that Earth does not occupy a privileged cosmic position, this constitutes the strongest available evidence for our own universe's homogeneity and isotropy, and hence for the foundation of current standard cosmological models. Strictly speaking, this conclusion has a potential flaw. While the Ehlers–Geren–Sachs theorem concerns only exactly isotropic measurements, it is known that the background radiation does have minute irregularities. This was addressed by a generalization published in 1995 by W. R. Stoeger, Roy Maartens and George Ellis, which shows that an analogous result holds for observers who measure a nearly isotropic background radiation, and can justly infer to live in a nearly FLRW universe. However the paper by Stoeger et al. assumes that derivatives of the cosmic background temperature multipoles are bounded in terms of the multipoles themselves. The derivatives of the multipoles are not directly accessible to us and would require observations over time and space intervals on cosmological scales. In 1999 John Wainwright, M. J. Hancock and Claes Uggla show a counterexample in the non-tilted perfect fluid case. Thus an almost isotropic cosmic microwave temperature does not imply an almost isotropic universe. Using the methods of Wainwright et al. Ho Lee, Ernesto Nungesser and John Stalker could show that they can be applied to Vlasov as well, which was the original matter model of the EGS-theorem.