LIGO Lo(g)Normal MACHO: Primordial Black Holes survive SN lensing
  constraints
  It has been claimed in Ref.[arXiv:1712.02240] that massive primordial black
holes (PBH) cannot constitute all of the dark matter (DM), because their
gravitational-lensing imprint on the Hubble diagram of type Ia supernovae (SN)
would be incompatible with present observations. In this paper, we critically
review those constraints and find several caveats on the analysis. First of
all, the constraints on the fraction $\alpha$ of PBH in matter seem to be
driven by a very restrictive choice of priors on the cosmological parameters.
In particular, the degeneracy between $\Omega_{\rm M}$ and $\alpha$ is ignored
and thus, by fixing $\Omega_{\rm M}$, transferred the constraining power of SN
magnitudes to $\alpha$. Furthermore, by considering more realistic physical
sizes for the type-Ia supernovae, we find an effect on the SN lensing
magnification distribution that leads to significantly looser constraints.
Moreover, considering a wide mass spectrum of PBH, such as a lognormal
distribution, further softens the constraints from SN lensing. Finally, we find
that the fraction of PBH that could constitute DM today is bounded by $f_{\rm
PBH} < 1.09\ (1.38)$, for JLA (Union 2.1) catalogs, and thus it is perfectly
compatible with an all-PBH dark matter scenario in the LIGO band.
