Opening the Window of Ultra-Light PBHs by Exorcising the Poltergeist

The hot Big Bang may have emerged from evaporation of primordial black holes (PBHs) lighter than ${10}^9$g. Standard monochromatic treatments predict nearly simultaneous evaporation, abrupt reheating, and a large Poltergeist scalar-induced gravitational wave signal. We confront this expectation with the irreducible collapse mass tail predicted by general relativity, $d{f}_{\mathrm{P}\mathrm{B}\mathrm{H}}\mathrm{/}d\ln M\propto M^{3.78}$, which smooths reheating, suppresses the signal by orders of magnitude, and reopens the ultra-light PBH window.