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I often see it implied that primordial black holes tend to be small compared to stellar masses;

Since primordial black holes did not form from stellar gravitational collapse, their masses can be far below stellar mass (c. 2×10^30 kg)

Primordial Black Holes

Given what we know about the state of the universe at the time of primordial black hole formation, and of the mechanisms by which they formed, what is the average/expected (in a statistical sense) size of such a black hole?

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  • $\begingroup$ Since they don't seem to exist, there may not be any way to decide on the parameters of a model that would predict this. $\endgroup$ – Ben Crowell Oct 2 at 13:53
  • $\begingroup$ @BenCrowell There is no real indication that they don't exist. $\endgroup$ – mmeent Oct 2 at 14:02
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The answer is pretty much anything you want. Models for their formation are flexible enough to allow pretty much any reasonable size. There are some practical limits. If they would too small, we would expect them to have evaporated by now. Obviously, they also can't have masses that are of the order of all the mass in the universe.

I've seen people seriously suggest primordial black holes as large as millions of solar masses as seeds for galaxy formation, an as light as couple of trillion kg to explain dark matter.

There are observation constraints that limit the fraction of the total mass density of the universe that could exist as primordial black holes though. Here is an example of a plot (from arXiv:1705.05567) showing the constraints (assuming all primordial black holes have the same mass).

enter image description here

Note that the validity of some of these bounds is subject of ongoing discussion. I'm no expert, so can't vouch for the validity of the particular bounds shown here. Anyway, anything between $10^{-17}$ and $10^2$ solar masses is still viable as being a some fraction of the total dark matter.

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