Gravitational Coupling and the Cosmological Constant

We deal with a dynamical mechanism in which a large cosmological constant, as suggested by inflationary scenarios, decays due to expansion of the universe. This mechanism has its origin in the gravitational coupling of the vacuum density. We assume that the vacuum couples anomalously to gravity that is the metric tensor that appears the gravitational part is not the same as that appears the matter part as suggested by weak equivalence principle. Instead, the two metric tensors are taken to be conformally related. We show that this provides a dynamical mechanism which works during expansion of the universe. We also consider some observational consequences of such a gravitational model.