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

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 $\mu$-distortion in the CMB spectrum. While the current bound on the average $\mu$-distortion is $\left|\bar{\mu }\right|\lesssim 10^{-4}$, the standard $\Lambda$CDM model predicts $\left|\bar{\mu }\right|\sim 10^{-8}$, which could possibly be detected in future missions. It is shown in this work that the non-observation of $\bar{\mu }$ beyond $\Lambda$CDM can place a new upper bound on the density of supermassive primordial black holes within the mass range $10^6{M}_{\odot }\lesssim M\lesssim 10^{15}{M}_{\odot }$. Furthermore, black holes with initial mass $M\gtrsim 10^{12}{M}_{\odot }$ could leave a pointlike distortion with $\mu \gtrsim 10^{-8}$ at an angular scale $\sim 1^{\circ }$ in CMB, and its non-observation would impose an even more stringent bound on the population of these stupendously large primordial black holes.

arXiv comment21 pages in REVTeX (V.4), 3 figures

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