Limits on primordial black holes from $\mu$ distortions in cosmic microwave background

TL;DR

This paper shows that the formation of primordial black holes in the mass range $10^5$ to $10^{12} M_{igodot}$ is strongly constrained by cosmic microwave background $d$ distortions, limiting their cosmological significance unless fluctuations are highly non-Gaussian.

Contribution

It provides new constraints on primordial black hole formation from $d$ distortions in the CMB, especially for Gaussian primordial fluctuations.

Findings

$d$ distortions severely limit PBHs in the mass range $10^5$ to $10^{12} M_{igodot}$

Gaussian primordial fluctuations cannot produce PBHs in this mass range without violating $d$ constraints

Non-Gaussian fluctuations or alternative formation mechanisms could evade these constraints

Abstract

If primordial black holes (PBHs) form directly from inhomogeneities in the early Universe, then the number in the mass range $10^5 -10^{12}M_{\odot}$ is severely constrained by upper limits to the $\mu$ distortion in the cosmic microwave background (CMB). This is because inhomogeneities on these scales will be dissipated by Silk damping in the redshift interval $5\times 10^4\lesssim z\lesssim2\times 10^6$. If the primordial fluctuations on a given mass scale have a Gaussian distribution and PBHs form on the high-$\sigma$ tail, as in the simplest scenarios, then the $\mu$ 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.