Abstract
In a variety of mechanisms generating primordial black holes, eachblack hole is expected to form along with a surrounding underdense region thatroughly compensates the black hole mass. This region will propagateoutwards and expand as a shell at the speed of sound in the homogeneous background. Dissipation of the shell due to Silk damping could lead todetectable μ-distortion in the CMB spectrum: if black holes are rare on the last scattering surface, the signal(s) would be pointlike; whereas if there are a sufficient number of them, we could have a uniform distortion in the CMB sky. While the currentbound on the average μ-distortion is |μ̅| ≲ 10-4,the standard ΛCDM model predicts |μ̅| ∼ 10-8,which could possibly be detected in future missions. It is shown inthis work that the non-observation of μ̅ beyond ΛCDMcan place a new upper bound on the density of supermassive primordialblack holes within the mass range 106 M ☉≲ M ≲ 1015 M ☉.Furthermore, black holes with initial mass M ≳ 1012 M ☉could leave a pointlike distortion with μ ≳10-8 at anangular scale ∼ 1° in CMB, and its non-observation wouldimpose an even more stringent bound on the population of these stupendously large primordialblack holes.
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