Reconstruction of potentials of the hybrid inflation in the light of
  primordial black hole formation
  The large enhancement of the primordial power spectrum of the curvature
perturbation can seed the formation of primordial black hole, that can play as
a dark matter component in the Universe. In multi-filed inflation models, the
curved trajectory of the scalar fields in the field space can generate a peak
in the power spectrum on small scales due to the existence of the isocurvature
perturbation. Here we show that a potential can be reconstructed from a given
power spectrum, which is made of a scale-invariant one on large scales and the
other function with a peak on small scales. In multi-field inflation models the
reconstructed potential may not be unique and we can find different potentials
from a given power spectrum.
