CMB constraints on ultra-light primordial black holes with extended mass
  distributions
  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 $\Lambda$CDM parameters to vary simultaneously with the PBH fraction and
mass, we show that exclusion bounds on the PBH fraction of DM $f_\text{PBH}$
are relaxed by up to an order of magnitude, compared to the case of fixed
$\Lambda$CDM parameters. We also give 95% exclusion regions for $f_\text{PBH}$
for a variety of mass distributions. In particular, for a uniform mass
distribution between $10^{15}$ and $10^{17}$ g, we find $f_\text{PBH} < 1.6
\times 10^{-5}$ when allowing $\Lambda$CDM parameters to vary.
