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 contribution we discuss how the parameter space of the model is constrained by providing viable scenarios for the first four of this list.