Consistent cosmology with Higgs thermal inflation in a minimal extension of the MSSM

We consider a class of supersymmetric inflation models, in which minimal gauged F-term hybrid inflation is coupled renormalisably to the minimal supersymmetric standard model (MSSM), with no extra ingredients; we call this class the ``minimal hybrid inflationary supersymmetric standard model'' (MHISSM). The singlet inflaton couples to the Higgs as well as the waterfall fields, supplying the Higgs μ-term. We show how such models can exit inflation to a vacuum characterised by large Higgs vevs, whose vacuum energy is controlled by supersymmetry-breaking. The true ground state is reached after an intervening period of thermal inflation along the Higgs flat direction, which has important consequences for the cosmology of the F-term inflation scenario. The scalar spectral index is reduced, with a value of approximately 0.976 in the case where the inflaton potential is dominated by the 1-loop radiative corrections. The reheat temperature following thermal inflation is about 109 GeV, which solves the gravitino overclosure problem. A Higgs condensate reduces the cosmic string mass per unit length, rendering it compatible with the Cosmic Microwave Background constraints without tuning the inflaton coupling. With the minimal U(1)' gauge symmetry in the inflation sector, where one of the waterfall fields generates a right-handed neutrino mass, we investigate the Higgs thermal inflation scenario in three popular supersymmetry-breaking schemes: AMSB, GMSB and the CMSSM, focusing on the implications for the gravitino bound. In AMSB enough gravitinos can be produced to account for the observed dark matter abundance through decays into neutralinos. In GMSB we find an upper bound on the gravitino mass of about a TeV, while in the CMSSM the thermally generated gravitinos are sub-dominant. When Big Bang Nucleosynthesis constraints are taken into account, the unstable gravitinos of AMSB and the CMSSM must have a mass O(10) TeV or greater, while in GMSB we find an upper bound on the gravitino mass of O(1) TeV