It has been claimed in Ref . [ arXiv:1712.02240 ] , that massive primordial black holes ( PBH ) can not 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 note , 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 _ { M } and \alpha was ignored and thus , by fixing \Omega _ { 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 _ { 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 .