Relativistic accretion and burdened primordial black holes

We examine the joint effects of relativistic accretion and memory-burdened evaporation on the evolution of primordial black holes (PBHs). The memory burden effect, which delays the evaporation by inducing a backreaction and making the evaporation rate scale as an inverse power law of the PBH entropy, opens up a new window that allows PBHs with $M \lesssim 10^{15}~\mathrm{g}$ to survive until the present epoch. Meanwhile, accretion increases the mass of PBHs, thereby enhancing their chances of survival for a given initial mass. We consider two main scenarios: one where PBHs evaporate completely before big bang nucleosynthesis, and another where PBHs persist until today. In the case of evaporation, we analyze the emission of dark matter (DM) and dark radiation (DR) during the process of evaporation. Conversely, in the other case, the surviving PBHs themselves can contribute as DM. We further investigate how relativistic and nonrelativistic accretion, together with memory-burdened evaporation, impact the parameter space of the emitted DM, the abundance of stable PBHs as DM, and the contribution of DR to the effective number of relativistic degrees of freedom, $\Delta N_{\mathrm{eff}}$.