  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.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology