The large-distance limit of the gravitational effective action in hyperbolic backgrounds

The one-loop effective action for D-dimensional quantum gravity with negative cosmological constant is investigated in spacetimes with compact hyperbolic spatial section. The explicit expansion of the effective action is derived as a power series of the curvature on the hyperbolic background, making use of heat-kernel and zeta-regularization techniques. We discuss, at one-loop level, the Coleman--Weinberg-type suppression of the cosmological constant, proposed by Taylor and Veneziano.