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.