Constraints on primordial black holes by distortions of the cosmic microwave background

The possible influence of primordial black hole (PBH) evaporations on cosmic microwave backgrounds (CMB) is investigated. The spectrum distortions of CMB from the blackbody spectrum are described by the chemical potential μ and the Compton parameter y. From COBE/FIRAS limits on μ and y, the power-law index n of primordial density fluctuations and the mass fraction of PBHs β 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 ζ_th=0.7 and ζ_th=1.2, respectively, for the PBH mass range between 2.7×10¹¹  g and 1.6×10¹²  g, and n<1.312 and n<1.343 in the thresholds of peaks ζ_th=0.7 and ζ_th=1.2, respectively, for the PBH mass range between 1.6×10¹²  g and 3.5×10¹³  g, which correspond to the comoving scales between 3×10^-18  Mpc and 4×10^-17  Mpc. The constraint on the PBH fraction, which is the direct probe of the amplitude of density fluctuations on these scales, stays at almost the same value as β<10^-21 in these mass ranges. It is also found that, with these constraints, UV photons injected by PBH evaporations are unlikely to ionize the majority of hydrogen atoms.