  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 potentials with a
prominent shift-symmetric part proportional to c- and a tiny violation,
proportional to c+, included in a logarithm with prefactor -N<0. It also offers
an explanation of mu term of the MSSM provided 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 1.8x10^13 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<=c+/c-<1/N and gravitino as light as 1 TeV.
