Limits on primordial black holes from $\mu$ distortions in cosmic microwave background

International audienceIf primordial black holes (PBHs) form directly from inhomogeneities in the early Universe, then the number in the mass range 105-1012 M⊙ is severely constrained by upper limits to the μ distortion in the cosmic microwave background (CMB). This is because inhomogeneities on these scales will be dissipated by Silk damping in the redshift interval 5×104≲z≲2×106. If the primordial fluctuations on a given mass scale have a Gaussian distribution and PBHs form on the high-σ tail, as in the simplest scenarios, then the μ constraints exclude PBHs in this mass range from playing any interesting cosmological role. Only if the fluctuations are highly non-Gaussian, or form through some mechanism unrelated to the primordial fluctuations, can this conclusion be obviated