CMB polarization non-Gaussianity from accreting primordial black holes

Primordial black holes (PBHs) would induce non-Gaussianity in the cosmic microwave background (CMB) by sourcing recombination perturbations spatially modulated by relative velocities between PBHs and the baryons they accrete. The leading non-Gaussian signatures are nonvanishing connected 4-point correlation functions, or trispectra. Earlier, we computed the CMB temperature trispectrum, and forecasted Planck to be more sensitive to it than to changes in the CMB temperature power spectrum for light enough PBHs. Excitingly, accreting PBHs would also induce non-Gaussianity in CMB polarization, and source both $E$ and $B$ modes, which we compute in this paper. We first calculate linear-response perturbations to the tensor-valued photon distribution function sourced by a general spatially varying ionization history, and apply our results to accreting PBHs. We then compute linear-order perturbations to the temperature and polarization 2-point functions sourced by inhomogeneities in recombination due to accreting PBHs; we find them to be negligible relative to their counterparts sourced by homogeneous perturbations to the ionization history. Lastly, we compute all CMB trispectra including temperature, $E$- and $B$-mode polarization at linear order in the PBH abundance. We forecast that including polarization data in a 4-point-function analysis would only increase Planck's sensitivity to accreting PBHs by a factor $\ensuremath{\sim}2$ relative to using temperature alone. As a consequence, we find that a search for PBHs using all temperature and polarization trispectra with Planck data would mostly not be competitive with current bounds from temperature and polarization power spectra. In contrast, we forecast that a CMB Stage-4 experiment would gain significant sensitivity to accreting PBHs through a 4-point-function search, in particular through the contributions of parity-odd trispectra including one $B$-mode field.