Constraints on Primordial Black Holes by Distortions of Cosmic Microwave Background

Hiroyuki Tashiro, Naoshi Sugiyama

Published 2008-01-21, updated 2008-07-11Version 2

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.