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 epoch of Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) photon decoupling. In our setup, one does not need to modify the scale-invariant inflationary power spectra; instead, a late phase transition in strongly interacting fermion-scalar fluid (which naturally occurs around red-shift $ 10^6 \leq \, z_{\scriptscriptstyle T} \, \leq 10^8$ ) creates an instability in the density perturbation as sound speed turns imaginary. As a result, the dark matter perturbation grows exponentially in sub-Compton scales. This follows the immediate formation of early dense dark matter halo, which finally evolves into PBH due to cooling through scalar radiation. We calculate the variance of the density perturbations and PBH fractional abundances $f(M)$ by using a non-monochromatic mass function. We find the peak of our PBH mass function lies between $10^{-16} - 10^{-14}$ solar mass for $ z_{\scriptscriptstyle T} \simeq 10^6$, and thus it can be 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 to PBH due to cooling through scalar radiation.