  A gauged U(1)_B-L symmetry predicts three right handed handed neutrinos and
its spontaneous breaking automatically yields the seesaw mechanism. In a
supersymmetric setting this breaking can be nicely linked with inflation to
yield deltaT/ T proportional to (M_B-L / M_P)^2, where M_B-L (M_P) denote the
B-L breaking (Planck) scale. Thus M_B-L is estimated to be of order 10^16 GeV,
and the heaviest right handed neutrino mass is less than or of order 10^14 GeV.
A second right handed neutrino turns out to have a mass of order 10-10^2 T_r,
where T_r (<~10^9 GeV) denotes the reheat temperature. A U(1) R symmetry plays
an essential role in implementing inflation and leptogenesis, resolving the
MSSM mu problem and eliminating dimension five nucleon decay. An unbroken Z_2
subgroup plays the role of matter parity. The scalar spectral index
n_s=0.99+-0.01 for the simplest models, while in smooth hybrid inflation
n_s>=0.97. The tensor to scalar ratio r is negligible, and dn_s/dlnk<~10^-3.
