On the relation between the isotropy of the CMB and the geometry of the universe

TL;DR

This paper explores the theoretical link between the near-uniformity of the cosmic microwave background and the universe's geometry, extending existing theorems and discussing their limitations in real-world observations.

Contribution

The authors derive new theorems extending the Ehlers-Geren-Sachs result to almost isotropic cases and analyze their applicability to the actual universe.

Findings

New theorems generalize the link between CMB isotropy and universe geometry.

The theorems do not directly apply to the real universe due to observational limitations.

CMB observations alone do not guarantee the universe's near homogeneity and isotropy.

Abstract

The near-isotropy of the cosmic microwave background (CMB) is considered to be the strongest indication for the homogeneity and isotropy of the universe, a cornerstone of most cosmological analysis. We derive new theorems which extend the Ehlers-Geren-Sachs result that an isotropic CMB implies that the universe is either stationary or homogeneous and isotropic, and its generalisation to the almost isotropic case. We discuss why the theorems do not apply to the real universe, and why the CMB observations do not imply that the universe would be nearly homogeneous and isotropic.