Primordial black hole constraints for extended mass functions
  We revisit the cosmological and astrophysical constraints on the fraction of
the dark matter in primordial black holes (PBHs) with an extended mass
function. We consider a variety of mass functions, all of which are described
by three parameters: a characteristic mass and width and a dark matter
fraction. Various observations then impose constraints on the dark matter
fraction as a function of the first two parameters. We show how these
constraints relate to those for a monochromatic mass function, demonstrating
that they usually become more stringent in the extended case than the
monochromatic one. Considering only the well-established bounds, and neglecting
the ones that depend on additional astrophysical assumptions, we find that
there are three mass windows, around $4\times 10^{-17}M_\odot,$ $2\times
10^{-14}M_\odot$ and $25-100M_\odot$, where PBHs can constitute all dark
matter. However, if one includes all the bounds, PBHs can only constitute of
order $10\%$ of the dark matter.
