Invariant random fields in vector bundles and application to cosmology
  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.
