Limits on primordial black holes from μ distortions in cosmic microwave background

If primordial black holes (PBHs) form directly from inhomogeneities in the early Universe, then the number in the mass range 10^5-10^12 M_ is severely constrained by upper limits to the distortion in the cosmic microwave background (CMB). This is because inhomogeneities on these scales will be dissipated by Silk damping in the redshift interval 510^4210^6. If the primordial fluctuations on a given mass scale have a Gaussian distribution and PBHs form on the high- tail, as in the simplest scenarios, then the 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.