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

TL;DR

This paper derives bounds on primordial black hole masses based on the trans-Planckian censorship conjecture, showing that certain PBH mass ranges for dark matter are incompatible with high inflationary scales.

Contribution

It establishes a universal lower bound on PBH mass from TCC constraints, independent of reheating details, and explores implications for dark matter.

Findings

Lower bound on PBH mass: M_PBH > γ(H_end/10^9 GeV)^2 M_sun

Current PBH dark matter window can be excluded if inflation scale > 10 TeV

Upper mass bound for PBHs formed in early matter-dominated era

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 noninstantaneous reheating history. In this paper we will show that, if the primordial black holes (PBHs) are formed 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 details 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.