Constraints on primordial black holes from Galactic gamma-ray background
  The fraction of the Universe going into primordial black holes (PBHs) with
initial mass M_* \approx 5 \times 10^{14} g, such that they are evaporating at
the present epoch, is strongly constrained by observations of both the
extragalactic and Galactic gamma-ray backgrounds. However, while the dominant
contribution to the extragalactic background comes from the time-integrated
emission of PBHs with initial mass M_*, the Galactic background is dominated by
the instantaneous emission of those with initial mass slightly larger than M_*
and current mass below M_*. Also, the instantaneous emission of PBHs smaller
than 0.4 M_* mostly comprises secondary particles produced by the decay of
directly emitted quark and gluon jets. These points were missed in the earlier
analysis by Lehoucq et al. using EGRET data. For a monochromatic PBH mass
function, with initial mass (1+\mu) M_* and \mu << 1, the current mass is
(3\mu)^{1/3} M_* and the Galactic background constrains the fraction of the
Universe going into PBHs as a function of \mu. However, the initial mass
function cannot be precisely monochromatic and even a tiny spread of mass
around M_* would generate a current low-mass tail of PBHs below M_*. This tail
would be the main contributor to the Galactic background, so we consider its
form and the associated constraints for a variety of scenarios with both
extended and nearly-monochromatic initial mass functions. In particular, we
consider a scenario in which the PBHs form from critical collapse and have a
mass function which peaks well above M_*. In this case, the largest PBHs could
provide the dark matter without the M_* ones exceeding the gamma-ray background
limits.
