$F_D$-Term Hybrid Inflation with Electroweak-Scale Lepton Number Violation

We study F-term hybrid inflation in a novel supersymmetric extension of the SM with a subdominant Fayet-Iliopoulos D-term. We call this particular form of inflation, in short, F_D-term hybrid inflation. The proposed model ties the mu-parameter of the MSSM to an universal lepton-number-violating Majorana mass, through the vacuum expectation value of the inflaton field which can naturally be of the electroweak scale. The late decays of the ultraheavy particles associated with the extra U(1) gauge group, which are abundantly produced during the preheating epoch, could lower the reheat temperature even up to 1 TeV, thereby avoiding the gravitino overproduction problem. The baryon asymmetry in the Universe can be explained through thermal electroweak-scale resonant leptogenesis, in a way independent of any pre-existing lepton- or baryon-number abundance. Further cosmological and particle-physics implications of the F_D-term hybrid model are briefly discussed.