$\mu$-distortion around stupendously large primordial black holes

Understand

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 $\mu$-distortion in the CMB spectrum.
• While the current bound on the average $\mu$-distortion is $\left| \bar{\mu}\right|\lesssim10^{-4}$, the standard $\Lambda$CDM model predicts $\left| \bar{\mu}\right|\sim10^{-8}$, which could possibly be detected in future missions.