On the connection between the cosmological constant and the gravitational constant in a theory of induced gravity

The path-integral formulation of quantum gravity has been utilized by Hawking to show how the effective cosmological constant Λsub(eff) may vanish. A closely related (but less general) discussion has been given independently by Baum, in terms of a scalar field phi. We extend these analyses to a model of induced gravity, in which the classical Hilbert lagrangian density (16πG)-1R is replaced by 1/2epsilonphi2R. If the effective potential has the Coleman-Weinberg form Vsub(eff) = 1/4lambdaphi4[ln(phi2/sigma2)-1/2] + const., then the most probable configuration is again the one for which Λsub(eff) vanishes. The induced gravitational constant is positive, and it is independent of temperature. (orig.)