  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.
