Formation and Abundance of Late-forming Primordial Black Holes as Dark Matter

We propose a novel mechanism where primordial black hole (PBH) dark matter is formed much later in the history of the universe, between the epochs of Big Bang nucleosynthesis and cosmic microwave background photon decoupling. In our setup, one does not need to modify the scale-invariant inflationary power spectra; instead, a late-phase transition in a strongly interacting fermion-scalar fluid (which occurs naturally around redshift 10(6) <= z ( T ) <= 10(8)) creates an instability in the density perturbation as the sound speed turns imaginary. As a result, the dark matter perturbation grows exponentially in sub-Compton scales. This follows the immediate formation of an early dense dark matter halo, which finally evolves into PBHs due to cooling through scalar radiation. We calculate the variance of the density perturbations and the PBH fractional abundances f(M) by using a nonmonochromatic mass function. We find that the peak of our PBH mass function lies between 10(-16) and 10(-14) solar mass for z ( T ) similar or equal to 10(6), and thus that it can constitute the entire dark matter of the universe. In PBH formation, one would expect a temporary phase where an attractive scalar balances the Fermi pressure. We numerically confirm that such a state indeed exists, and we find the radius and density profile of the temporary static structure of the dark matter halo, which finally evolves into PBHs due to cooling through scalar radiation.