Proving Almost-Homogeneity of the Universe and Placing Limits on Its \\ Anisotropy and Inhomogeneity
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**Session 118 -- Cosmic Micorwave Background**
*Oral presentation, Thursday, 12, 1995, 2:00pm - 3:30pm*

## [118.07] Proving Almost-Homogeneity of the Universe and Placing Limits on Its \\ Anisotropy and Inhomogeneity

*W. R. Stoeger (Vatican Obs.), G. F. R. Ellis (University of Cape Town), R. Maartens (University of Portsmouth)*
We show that if all fundamental observers measure the cosmic microwave
background radiation to be almost isotropic in a region of an expanding
universe, then that universe is almost spatially homogeneous and isotropic
in that region. This demonstrates the stability of the important exact
result of this type previously proved by Ehlers, Geren and Sachs (1968), and
formalizes the way in which almost-isotropy of the background radiation gives
evidence that the universe is almost a Friedmann-Lema\^{i}tre-Robertson-
Walker (FLRW) space-time. This is the needed foundation for all recent
analyses, based on the Sachs-Wolfe effect, of how background anisotropies
relate to growing density inhomogeneities in an almost-FLRW expanding universe.

By using this approach, through which we can consider directly how matter
imposes anisotropies on freely propagating background radiation, we also
show how background anisotropy measurements place limits on the deviations
of the universe from an FLRW geometry. This limits are not as detailed as
those determined by the usual Sachs-Wolfe approach, but they are more model-
independent. \\

Ehlers, J., Geren, P., and Sachs, R. K. 1968, J. Math. Phys., 9, 1344.

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