Scaling behavior of semiclassical gravity

Using the idea of metric scaling the scaling behavior of the stress tensor of a scalar quantum field is examined in curved space-time. The renormalization of the stress tensor results in a departure from naive scaling. The process of renormalizing the stress tensor is viewed as being equivalent to renormalizing the coupling constants in the Lagrangian for gravity (with terms quadratic in the curvature included). Thus the scaling of the stress tensor is interpreted as a nonnaive scaling of these coupling constants. In particular, it is found that the cosmological constant and the gravitational constant approach UV fixed points. The constants associated with the terms which are quadratic in the curvature logarithmically diverge. This suggests that quantum gravity is asymptotically scale invariant. (author)