Way-out to the gravitino problem in intersecting D-brane Pati–Salam models

Abstract

We discuss the gravitino problem in the context of the exotic see-saw mechanism for neutrinos and leptogenesis, UV completed by intersecting D-branes Pati–Salam models. In the exotic see-saw model, supersymmetry is broken at high scales M[Formula: see text] 109 GeV and this seems in contradiction with gravitino bounds from inflation and baryogenesis. However, if gravitino is the lightest stable supersymmetric particle, it will not decay into other SUSY particles, avoiding the gravitino problem and providing a good cold dark matter (CDM). Gravitini are super heavy dark particles and they can be produced by non-adiabatic expansion during inflation. Intriguingly, from bounds on the correct abundance of dark matter (DM), we also constrain the neutrino sector. We set a limit on the exotic instantonic coupling of [Formula: see text] 10[Formula: see text]–10[Formula: see text]. This also sets constrains on the Calabi–Yau compactifications and on the string scale. This model strongly motivates very high energy DM indirect detection of neutrini and photons of 10[Formula: see text]–10[Formula: see text] GeV: gravitini can decay on them in a cosmological time because of soft R-parity breaking effective operators.