The superweak force is a minimal, anomaly-free U(1) extension of the
standard model, designed to explain the origin of (i) neutrino
masses and mixing matrix elements, (ii) dark matter, (iii) cosmic
inflation, (iv) stabilization of the electroweak vacuum and (v)
leptogenesis. In this talk we discuss how the parameter space of the
model is constrained by providing viable scenarios for the first four of
this list.