Abstract
In a variety of mechanisms generating primordial black holes, each
black hole is expected to form along with a surrounding underdense region that
roughly compensates the black hole mass. This region will propagate
outwards and expand as a shell at the speed of sound in the homogeneous background. Dissipation of the shell due to Silk damping could lead to
detectable 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 current
bound 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 in
this work that the non-observation of μ̅ beyond ΛCDM
can place a new upper bound on the density of supermassive primordial
black 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 an
angular scale ∼ 1° in CMB, and its non-observation would
impose an even more stringent bound on the population of these stupendously large primordial
black holes.