Non-gaussianity and B-mode polarization are particularly interesting features
of the cosmic microwave background, as -- at least in the standard model of
cosmology -- their only sources to first order in cosmological perturbation
theory are primordial, possibly generated during inflation. If the primordial
sources are small, the question arises how large is the non-gaussianity and
B-mode background induced in second-order from the initially gaussian and
scalar perturbations. In this paper we derive the Boltzmann hierarchy for the
microwave background photon phase-space distributions at second order in
cosmological perturbation theory including the complete polarization
information, providing the basis for further numerical studies. As an aside we
note that the second-order collision term contains new sources of B-mode
polarization and that no polarization persists in the tight-coupling limit.Comment: LaTeX, 33 page
