Abstract
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.