The primordial black holes (PBHs) are the topic which has attracted many scientists for a long time.
They have not been detected yet, but they might be produced in the early radiation-dominated era
by the gravitational collapse of overdense Hubble patches.
More massive PBHs than 10^15 g can survive to the present time against the Hawking evaporation
and they can be a main component of dark matter or seeds of supermassive black holes for example.
As an implementation mechanism, the formation of such massive PBHs in hybrid inflation has been studied by many authors.
Hybrid inflation is the inflationary model which is ended by the 2nd order phase transition of the waterfall field.
Around the phase transition critical point, the effective potential of the inflatons becomes extremely flat
and large perturbations which would cause PBH formation have been thought to be produced.
However, since the perturbative expansions w.r.t. the inflaton fields are broken down around the critical point,
there had been no quantitatively complete works yet.
Recently we proposed a non-perturbative algorithm to calculate the power spectrum of the curvature perturbations
by combining the stochastic and delta N formalism (http://arxiv.org/abs/1308.4754),
and successfully obtained the power spectrum around the critical point in hybrid inflation (http://arxiv.org/abs/1405.2187).
With use of these results, we have proceeded further investigations
and we found that massive PBHs are rather overproduced in hybrid inflation,
that is, massive PBHs cannot be produced with appropriate abundance in hybrid inflation (http://arxiv.org/abs/1512.03515).
That is our main conclusions.