Bipolar harmonic encoding of CMB correlation patterns

Deviations from statistical isotropy can be modeled in various ways, for instance, anisotropic cosmological models (Bianchi models), compact topologies, and presence of primordial magnetic field. Signature of anisotropy manifests itself in cosmic microwave background correlation patterns. Here we explore the symmetries of the correlation function and its implications on the observable measures constructed within the bipolar harmonic formalism for these variety of models. Different quantifiers within the bipolar harmonic representation are used to distinguish between plausible models of breakdown of statistical isotropy and as a spectroscopic tool for discriminating between distinct cosmic topology.