Primordial Black Holes And Gravitational Waves Based On No-Scale
  Supergravity
  In this paper we present a class of models in order to explain the production
of Primordial Black Holes (PBHs) and Gravitational Waves (GWs) in the Universe.
These models are based on no-scale theory. 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 and
GWs. As it is known in the literature there is an important unification of the
no-scale models, which leads to the Starobinsky effective scalar potential
based on the coset SU(2,1)/SU(2)$\times$U(1). We use this unification in order
to additionally explain the generation of PBHs and GWs. Concretely, 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 GWs 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) as well as the unification between the models which
are yielded this coset. We numerically evaluate the scalar power spectra with
the effective scalar potential based on this theory. Furthermore, we evaluate
the fractional abundances of PBHs by comparing two methods the Press-Schechter
approach and the peak theory, while focusing on explaining the dark matter in
the Universe. By using the resulting scalar power spectrum we evaluate the
amount of GWs. All models are in complete consistence with Planck constraints.
