Anatomy of $F_D$-Term Hybrid Inflation

We analyze the cosmological implications of F-term hybrid inflation with a subdominant Fayet--Iliopoulos D-term whose presence explicitly breaks a D-parity in the inflaton-waterfall sector. This scenario of inflation, which is called F_D-term hybrid model for brevity, can naturally predict lepton number violation at the electroweak scale, by tying the mu-parameter of the MSSM to an SO(3)-symmetric Majorana mass m_N, via the vacuum expectation value of the inflaton field. We show how a negative Hubble-induced mass term in a next-to-minimal extension of supergravity helps to accommodate the present CMB data and considerably weaken the strict constraints on the theoretical parameters, resulting from cosmic string effects on the power spectrum P_R. The usual gravitino overabundance constraint may be significantly relaxed in this model, once the enormous entropy release from the late decays of the ultraheavy waterfall gauge particles is properly considered. As the Universe enters a second thermalization phase involving a very low reheat temperature, which might be as low as about 0.3 TeV, thermal electroweak-scale resonant leptogenesis provides a viable mechanism for successful baryogenesis, while thermal right-handed sneutrinos emerge as new possible candidates for solving the cold dark matter problem. In~addition, we discuss grand unified theory realizations of F_D-term hybrid inflation devoid of cosmic strings and monopoles, based on the complete breaking of an SU(2) subgroup. The F_D-term hybrid model offers rich particle-physics phenomenology, which could be probed at high-energy colliders, as well as in low-energy experiments of lepton flavour or number violation.