Invariant random fields in vector bundles and application to cosmology

Abstract

We develop the theory of invariant random fields in vector bundles. The spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group $G$ is obtained. We discuss an application to the theory of cosmic microwave background, where $G=SO(3)$. A theorem about equivalence of two different groups of assumptions in cosmological theories is proved.

39 pages, 3 tables

References in corpus (3)

• Theory of Cosmic Microwave Background Polarization
• Anisotropies in the Cosmic Microwave Background
• Lecture notes on the physics of cosmic microwave background anisotropies

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