Constraints on Primordial Black Holes by Distortions of Cosmic Microwave Background

TL;DR

This paper constrains primordial black hole properties using cosmic microwave background distortions, limiting the primordial density fluctuation spectrum and PBH abundance, and assessing their impact on cosmic ionization history.

Contribution

It provides new constraints on the primordial density fluctuation spectrum and PBH abundance based on CMB spectral distortions, employing peak theory for PBH formation.

Findings

Constraints on spectral index n: less than 1.304 to 1.343 depending on parameters.

PBH mass fraction constrained to be less than 10^{-21}.

PBH evaporation unlikely to cause significant hydrogen ionization after recombination.

Abstract

Possible influence of primordial black hole (PBH) evaporations on cosmic microwave background (CMB) is investigated. The spectrum distortions of CMB from the black-body spectrum are described by the chemical potential $\mu$ and the Compton parameter $y$. From COBE/FIRAS limits on $\mu$ and $y$, the power law index $n$ of primordial density fluctuations and the mass fraction of PBHs $\beta$ are constrained by employing the peak theory for the formation process of PBHs. Constraints set here are $n < 1.304$ and $n<1.333$ in the thresholds of peaks $\zeta_{\rm th} =0.7$ and $\zeta_{\rm th} =1.2$, respectively, for the PBH mass range between $2.7\times 10^{11}$g and $1.6 \times 10^{12}$g, and $n < 1.312$ and $n<1.343$ in the thresholds of peaks $\zeta_{\rm th} =0.7$ and $\zeta_{\rm th} =1.2$, respectively, for the PBH mass range between $1.6 \times 10^{12} {\rm g}$ and $3.5\times 10^{13}$g, which correspond to the comoving scales between $3 \times 10^{-18}$Mpc and $ 4\times 10^{-17}$Mpc. The constraint on the PBH fraction, which is the direct probe of the amplitude of density fluctuations in these scales, stays an almost same value as $\beta<10^{-21}$ in these mass ranges. It is also found that, with these constraints, UV photons injected by PBH evaporations are unlikely ionize vast hydrogen atoms after recombination.