Mass bound for primordial black hole from trans-Planckian censorship conjecture

Abstract

The recently proposed trans-Planckian censorship conjecture (TCC) imposes a strong constraint on the inflationary Hubble scale, of which the upper bound could be largely relaxed by considering a non-instantaneous reheating history. In this letter we will show that, if the primordial black holes (PBHs) are collapsed at reentry in the radiation-dominated era from the enhanced curvature perturbations at small scales, the TCC would impose a lower bound on the PBH mass \(M_\mathrm{PBH}>\gamma(H_\mathrm{end}/10^9\,\mathrm{GeV})^2\,M_\odot\) regardless of the detail for reheating history, where \(\gamma\) is the collapse efficiency factor and \(H_\mathrm{end}\) is the Hubble scale at the end of inflation. In particular, the current open window for PBHs to make up all the cold dark matter could be totally ruled out if the inflationary Hubble scale is larger than 10 TeV. For the case of PBHs formed in an early matter-dominated era, an upper mass bound is obtained.