  We present a solution of the mu problem within a supersymmetric model based
on the SU(2)_L x SU(2)_R x U(1)_{B-L} gauge group. We show that this solution
implies a built-in hybrid inflationary scenario, which may result in a
successful baryogenesis via leptogenesis. Baryon number is essentially
conserved as a result of an R-symmetry. Neutrinos with mass in the eV range can
provide the `hot' dark matter component.
