Primordial Black Hole Abundance from Reionization

Abstract

We derive robust constraints on the initial abundance of evaporating primordial black holes (PBHs) using the reionization history of the Universe as a cosmological probe. We focus on PBHs that inject electromagnetic (EM) energy into the intergalactic medium (IGM) after recombination, in the mass range $3.2\times 10^{13}\,\mathrm{g} \lesssim M_{\rm PBH} \lesssim 5\times 10^{14}\,\mathrm{g}$. For each PBH mass, we compute the redshift-dependent energy injection from Hawking evaporation using \texttt{BlackHawk}, fully accounting for the time evolution of the PBH mass and the complete spectrum of emitted Standard Model particles and gravitons. The resulting photons and electrons are propagated through the primordial plasma using \texttt{DarkHistory}, which self-consistently models EM cascades and determines the fraction of injected energy deposited into ionization, excitation, and heating of the IGM. These modifications to the ionization and thermal histories are incorporated into a Gaussian Process reconstruction of the free-electron fraction based on low-$\ell$ CMB polarization data from the \textit{Planck} mission. This non-parametric approach allows for a statistically well-defined separation between exotic high-redshift energy injection and late-time astrophysical reionization, allowing PBH evaporation to be constrained through its contribution to the high-redshift optical depth. Requiring consistency with current CMB measurements, we obtain upper limits on the initial PBH abundance that are robust against reionization modeling uncertainties and systematically more conservative than existing bounds, reflecting the fully numerical and time-dependent treatment of Hawking evaporation and energy deposition. Our results demonstrate the power of reionization observables as a precision probe of PBH evaporation and other scenarios involving late-time energy injection.