  We study the reheating and leptogenesis in the case of a vector inflaton. We
concentrate on particle production during the phase of oscillating background,
especially gravitational production induced by the presence of non-minimal
coupling imposed by an isotropic and homogeneous Universe. Including processes
involving the exchange of graviton, we then extend our study to decay into
fermions via direct or anomalous couplings. The necessity of non-minimal
gravitational coupling and the gauge nature of couplings to fermions implies a
much richer phenomenology than for a scalar inflaton.
