Boosting the optical depth to Thomson scattering with primordial black hole evaporation at high redshift

BAO and CMB data are somewhat discrepant when interpreted in the context of cdm, discrepancies that show up as a `matter density deficit' and as a `CMB lensing excess'. One possible resolution is an increased optical depth to scattering off of free electrons in the post-recombination universe, tau, a possibility raised by Sailer et al. 2025 and Jhaveri et al. 2025. Since Planck measurements of the low- polarization `reionization bump' already constrain tau from standard stellar-driven reionization at z<10, we investigate additional optical depth sourced by transient or partial reionization at higher redshift from exotic processes. For specificity, we explore the impact of Hawking radiation from a monochromatic spectrum of primordial black holes, retaining the high- TT/TE/EE data that constrain such histories and varying the reionization redshift jointly. We find that the CMB data do not significantly prefer these additional signals: the boost is at most tau 0.008, well short of the tau 0.03 that would completely eliminate the moderate discrepancy. The matter density deficit and the lensing excess are not significantly eased: we explain why, tracing it to compensation from the reionization redshift and the residual PBH signal at > 30.