CMB constraints on ultra-light primordial black holes with extended mass distributions
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(2019)cite arxiv:1907.06485.

We examine the effects ultra-light primordial black holes (PBHs) have on the anisotropies of the cosmic microwave background (CMB). PBHs in the mass range of $10^15$ to $10^17$ g emit Hawking radiation in the early Universe, modifying the standard recombination history. This leads to a damping of small-scale temperature and polarisation anisotropies and enhances large-scale polarisation fluctuations. As some models of inflation predict PBHs with a range of masses, we investigate the impacts of extended mass distributions on PBH abundance constraints. We model PBH energy injection using a ground-up approach incorporating species-dependent deposition efficiencies. By allowing the $Łambda$CDM parameters to vary simultaneously with the PBH fraction and mass, we show that exclusion bounds on the PBH fraction of DM $f_PBH$ are relaxed by up to an order of magnitude, compared to the case of fixed $Łambda$CDM parameters. We also give 95% exclusion regions for $f_PBH$ for a variety of mass distributions. In particular, for a uniform mass distribution between $10^15$ and $10^17$ g, we find $f_PBH < 1.6 10^-5$ when allowing $Łambda$CDM parameters to vary.
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