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.