  We propose a scenario where dark matter (DM) with a wide mass range from a
few keV to PeV can be produced solely from evaporating primordial black holes
(PBH), while being consistent with the required free streaming length for
structure formation. If DM does not have any other interactions apart from
gravity and the universe has a PBH dominated phase at early epoch, then PBH
evaporation typically leads to overproduction of DM in this mass range. By
incorporating this gravitational DM within a Type-I seesaw scenario with three
right handed neutrinos (RHN), we bring the abundance of PBH generated DM within
observed limits by late entropy injection due to decay of one of the RHNs,
acting as the diluter. The diluter, due to its feeble coupling with the bath
particles, gets produced primarily from the PBH evaporation thereby leading to
the second stage of early matter domination after the end of PBH dominated era.
The other two RHNs contribute to the origin of light neutrino mass and also
lead to the observed baryon asymmetry via leptogenesis with contributions from
both thermally and PBH generated RHNs. The criteria of DM relic and baryon
asymmetry can be satisfied simultaneously if DM mass gets restricted to a
ballpark in the MeV-GeV regime with the requirement of resonant leptogenesis
for heavier DM mass in order to survive the large entropy dilution at late
epochs.
