A novel formulation of the PBH mass function
  Computations of the primordial black hole (PBH) mass function discussed in
the literature have conceptual issues. They stem from that the mass function is
a differential quantity and the standard criterion of the PBH formation from
the seed primordial fluctuations cannot be directly applied to the computation
of the differential quantities. We propose a new criterion of the PBH formation
which is an addition of one extra condition to the existing one. By doing this,
we derive a formal expression of the PBH mass function without introducing any
ambiguous interpretations which exist in the previous studies. Once the
underlying primordial fluctuations are specified, the PBH mass function can be
in principle determined by the new formula. As a demonstration of our
formulation, we compute the PBH mass function analytically for the case where
the perturbations are Gaussian and the space is one dimension.
