  We focus on a simple, natural and predictive T model of inflation in
Supergravity employing as inflaton the Higgs field which leads to the
spontaneous breaking of a U(1)_(B-L) symmetry at the SUSY GUT scale. We use a
renormalizable superpotential, fixed by a U(1) R symmetry, and a Kahler
potential which parameterizes the Kahler manifold
SU(2,1)/(SU(2)xU(1))x(SU(2)/U(1)) with scalar curvature R_K=-6/N+2/N_0 where
0<N_0<6. The spectral index ns turns out to be close to its present central
observational value and the tensor-to-scalar ratio r increases with N<36. The
model can be nicely linked to MSSM offering an explanation of the magnitude of
the mu parameter consistently with phenomenological data. It also allows for
baryogenesis via non-thermal leptogenesis with gravitino as light as 1 TeV.
