Mechanisms of Producing Primordial Black Holes By Breaking The
  SU(2,1)/SU(2)$\times$U(1) Symmetry
  In this paper we present a class of potentials derived by no-scale
supergravity in order to explain the production of primordial black holes
(PBHs) in the Universe. By breaking the SU(2,1)/SU(2)$\times$U(1) symmetry we
fix one of the two chiral fields and we derive effective scalar potentials
which are capable of generating PBHs. Specifically, we modify well-known
superpotentials, which reduce to Starobinsky-like effective scalar potentials.
Thus, we derive scalar potentials which, on the one hand, explain the
production of PBHs and, on the other hand, they conserve the transformation
laws, which yield from the parametrization of the coset
SU(2,1)/SU(2)$\times$U(1). Moreover, we generate PBHs by modifying the kinetic
term of the Langrangian (or the K\"ahler potential) and we keep the
superpotentials unmodified. In all cases we evaluate the fractional abundances
of PBHs by comparing Press-Schechter approach and peak theory, while focusing
on explaining the dark matter in the Universe. All models are in complete
consistence with Planck constraints.
