The cosmological evolution of primordial black holes (PBHs) is considered. A
comprehensive view of the accretion and evaporation histories of PBHs across
the entire cosmic history is presented, with focus on the critical mass holes.
The critical mass of a PBH for current era evaporation is $M_{cr}\sim
5.1\times10^{14}$ g. Across cosmic time such a black hole will not accrete
radiation or matter in sufficient quantity to hasten the inevitable
evaporation, if the black hole remains within an average volume of the
universe. The accretion rate onto PBHs is most sensitive to the mass of the
hole, the sound speed in the cosmological fluid, and the energy density of the
accreted components. It is not easy for a PBH to accrete the average
cosmological fluid to reach $30M_\odot$ by $z\sim0.1$, the approximate mass and
redshift of the merging BHs that were the sources of the gravitational wave
events GW150914 and GW151226. A PBH located in an overdense region can undergo
enhanced accretion leading to the possibility of growing by many orders of
magnitude across cosmic history. Thus, two merging PBHs are a plausible source
for the observed gravitational wave events. However, it is difficult for
isolated PBHs to grow to supermassive black holes (SMBHs) at high redshift with
masses large enough to fit observational constraints.Comment: Resubmitted after correcting an error in the previous version;
matches published version in the Journal of High Energy Astrophysics; 33
pages, 5 figures, 3 table