Why is a primordial black hole's mass of the same order as the horizon mass in the early universe? I am reading a paper on primordial black holes (PBHs), and it says that PBHs should form during the first second of the universe with masses of the same order of magnitude as the horizon mass.
I couldn't convince myself why this is true and didn't find any explanation for the claim.
Does anyone have an explanation?
 A: The early universe was dominated by radiation, that is, particles moving at or close to the speed of light. Such particles exert a huge amount of pressure, relative to their energy density. This pressure quickly smooths out any variations in the density of the universe. No black holes can form under those conditions.
The standard primordial black hole formation scenario avoids this challenge in the following way. If a region of excess density is larger than the cosmological horizon, its different parts are not in causal contact. Therefore, it cannot evolve, instead remaining frozen in time. When the horizon finally grows to the size of this region, it faces two scenarios. If the region is not dense enough, the excess density gets smoothed out by the radiation pressure. However, for a particularly extreme density excess, its gravitational attraction defeats the radiation pressure and it quickly collapses into a black hole. Thus, a primordial black hole forming by this mechanism always forms from a horizon-sized patch.
