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

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.

5 pages. v2: Corrected an error in the proof, added references and clarifications

References in corpus (4)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Relativistic cosmology and large-scale structure
• Accelerated expansion from structure formation
• Evaluating backreaction with the peak model of structure formation

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• The quadrupole in the local Hubble parameter: first constraints using Type Ia supernova data and forecasts for future surveys
• Evaluating backreaction with the ellipsoidal collapse model
• Backreaction and the Covariant Formalism of General Relativity
• On almost Ehlers-Geren-Sachs theorems
• Redshift and gauge choice