Constraining Primordial Black-Hole Bombs through Spectral Distortions of the Cosmic Microwave Background

TL;DR

This paper investigates how superradiant instabilities of primordial black holes could cause spectral distortions in the cosmic microwave background, providing new constraints on their abundance and spin properties.

Contribution

It introduces a novel method to constrain spinning primordial black holes using CMB spectral distortions caused by superradiance-induced photon trapping and release.

Findings

Upper limits on PBH dark matter fraction derived from COBE/FIRAS data.

Constraints are tighter for maximally-spinning PBHs than previous microlensing bounds.

Future PIXIE data could significantly improve these constraints.

Abstract

We consider the imprint of superradiant instabilities of nonevaporating primordial black holes (PBHs) on the spectrum of the cosmic microwave background (CMB). In the radiation dominated era, PBHs are surrounded by a roughly homogeneous cosmic plasma which endows photons with an effective mass through the plasma frequency. In this setting, spinning PBHs are unstable to a spontaneous spindown through the well-known "black-hole bomb" mechanism. At linear level, the photon density is trapped by the effective photon mass and grows exponentially in time due to superradiance. As the plasma density declines due to cosmic expansion, the associated energy around PBHs is released and dissipated in the CMB. We evaluate the resulting spectral distortions of the CMB in the redshift range 10^3 < z < 2x10^6. Using the existing COBE/FIRAS bounds on CMB spectral distortions, we derive upper limits on the fraction of dark matter that can be associated with spinning PBHs in the mass range 10^{-8}*Msun < M < 0.2*Msin. For maximally-spinning PBHs, our limits are much tighter than those derived from microlensing or other methods. Future data from the proposed PIXIE mission could improve our limits by several orders of magnitude.