Predictions for a Low-mass Cutoff for the Primordial Black Hole Mass Spectrum

In this note we outline how a modest violation in the conservation of mass during the merger of two PBHs affects the PBH mass spectrum that we previously obtained using a Boltzmann equation model for the evolution of the mass spectrum with no mass loss. We find that if the initial cosmological redshift is on the order 10$^{12}$, then the fraction of primordial holes with masses greater than $10^{3}$ solar masses appears be close to what is required to provide the seeds for galaxies. In addition we note that as a result of rapid collisions and strong coupling to electromagnetic radiation for temperatures $>$ GeV (Chapline 2018), there will be an effective low mass cutoff in the mass spectrum for PBH masses less than a certain PBH mass less than than $0.1M_{\odot}$. We also point out that this cutoff in the mass spectrum below $\sim 0.1 M_\odot$ can be confirmed by combining future microlensing observations from the Roman Space Telescope and the Vera C. Rubin Observatory with astrometric observations.