CMB Bounds on Primordial Black Holes via Radiation Capture

Abstract

We explore the capture of neutrinos and photons in the cosmic neutrino and photon background by primordial black holes (PBHs). We model this phenomenon as a gravitational interaction that effectively modifies the continuity equations for radiation and PBH densities and the cosmic expansion history. We find that the observability of this modified cosmic history is highly sensitive to PBH mass, and only extraordinarily massive PBHs would leave observable trace on the temperature and E-mode polarization of the cosmic microwave background (CMB). Specifically, Planck data restrict PBH abundance to $f_{\rm pbh}\lesssim 10^{-1}$ for PBH masses above $10^{15} M_\odot$, getting considerably tighter for higher masses. We expect substantial improvement as high-resolution measurements of larger CMB multipoles become available. A future cosmic-variance-limited experiment, with $\ell_{\rm max}=7000$, would set $f_{\rm pbh}\lesssim 10^{-1}-8\times 10^{-5}$ (for the fiducial $Λ$CDM cosmology) across $10^{13}-10^{18}M_\odot$. These constraints would be comparable to the current limits at the high-mass end of the spectrum [Carr et al, 2026]. The gravitational interaction of PBHS with the cosmic background radiation and its imprints on CMB would thus provide an independent complementary probe of extraordinarily massive PBH abundance.