Gravitational Waves, mu Term and Leptogenesis from B - L Higgs Inflation in Supergravity

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 quadratic Kahler potential with a prominent shift-symmetric part proportional to c(-) and a tiny violation, proportional to c(+), included in a logarithm with prefactor -N < 0. 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 neutrino with masses lower than 1.8 x 10(13) GeV. Our scenario can be confronted with the current data on the inflationary observables, the baryon asymmetry of the universe, the gravitino limit on the reheating temperature and the data on the neutrino oscillation parameters, for 0.012 less than or similar to c(+)/c(-) less than or similar to 1/N and gravitino as light as 1 TeV.