B-L Higgs Inflation in Supergravity With Several Consequences

We consider a renormalizable extension of the minimal supersymmetric standard model endowed by an R and a gauged B - L symmetry. The model incorporates chaotic inflation driven by a quartic potential, associated with the Higgs field which leads to a spontaneous breaking of U(1)B-L, and yields possibly detectable gravitational waves. We employ semi-logarithmic Kahler potentials with an enhanced symmetry which include only quadratic terms and integer prefactor for the logarithms. An explanation of the mu term of the MSSM is also provided, consistently with the low energy phenomenology, under the condition that one related parameter in the superpotential is somewhat small. Baryogenesis occurs via non-thermal leptogenesis which is realized by the inflaton's decay to the lightest or next-to-lightest right-handed neutrinos.