Induced-gravity GUT-scale Higgs inflation in supergravity

Models of induced-gravity inflation are formulated within Supergravity employing as inflaton the Higgs field which leads to a spontaneous breaking of a (U(1)_{B-L}) symmetry at (M_mathrm{GUT}=2cdot 10^{16}~{mathrm{GeV}}). We use a renormalizable superpotential, fixed by a U(1) R symmetry, and Kähler potentials which exhibit a quadratic non-minimal coupling to gravity with or without an independent kinetic mixing in the inflaton sector. In both cases we find inflationary solutions of Starobinsky type whereas in the latter case, others (more marginal) which resemble those of linear inflation arise too. In all cases the inflaton mass is predicted to be of the order of (10^{13}~{mathrm{GeV}}). Extending the superpotential of the model with suitable terms, we show how the MSSM (mu ) parameter can be generated. Also, non-thermal leptogenesis can be successfully realized, provided that the gravitino is heavier than about (10~{mathrm{TeV}}).