Inflation, SUSY breaking, and primordial black holes in modified supergravity coupled to chiral matter

Abstract: We propose a novel model of the modified (Starobinsky-like) old-minimal-type supergravity coupled to a chiral matter superfield, that can {\it simultaneously} describe multi-field inflation, primordial black hole (PBH) formation, dark matter (DM), and spontaneous supersymmetry (SUSY) breaking after inflation in a Minkowski vacuum. The PBH masses in our supergravity model of double slow-roll inflation, with a short phase of "ultra-slow-roll" between two slow-roll phases, are close to $10^{18}$ g. We find that a significant PBH fraction in the allowed mass window can be supplemented by spontaneous SUSY breaking in the vacuum with the gravitino mass close to the scalaron (inflaton) mass M of the order $10^{13}$ GeV. Our supergravity model favors the {\it composite} nature of DM as a mixture of PBH and heavy gravitinos as the lightest SUSY particles. The composite DM significantly relaxes fine-tuning needed for the whole PBH-DM. The PBH-DM fraction is derived, and the second-order gravitational wave background induced by the enhanced scalar perturbations is calculated. Those gravitational waves may be accessible by the future space-based gravitational interferometers.