Physics Beyond The Standard Model with Circular Polarization in the CMB
  and CMB-21cm Cross-Correlation
  Circular polarization is a relatively unexplored realm of CMB physics. Given
the substantial community effort towards building next generation CMB
polarization experiments, including those which will be sensitive to circular
polarization, it behooves theorists to understand the possible sources and
relevant physics of circular polarization, as encoded in the Stokes V
parameter. In this work we develop and derive the requisite formalism, namely
the Boltzmann hierarchy for V-mode scalar, vector, and tensor, anisotropies. We
derive the V-mode anisotropies induced by a general source term, and
demonstrate how existing proposals for the generation of V can be incorporated
as source terms in the Boltzmann hierarchy. A subset of these effects may be
correlated with 21cm intensity; we provide a worked example and derive an
estimator to extract this information from observations. We conclude by
computing the CMB TV cross-correlation generated by axions, and find a relation
between TV and VV spectra in axion models.
