Path-Integral Measure of Linearized Gravity in Curved Spacetime

Abstract

The path-integral measure of linearized gravity around a saddle-point background with the cosmological term is considered in order to study the conformal rotation prescription proposed by Gibbons, Hawking and Perry. It is also argued that the most generally used measure, i.e., the covariant path-integral measure, does not give us a one-loop partition function which the only physical variables contribute and that its path integral fails to keep the cancellation of contributions between the Faddeev-Popov ghosts and the unphysical variables of the linearized gravitational field, although it has a coordinate invariant measure. In de~Sitter spacetime, it is shown that the uncancellation factor can be understood as a nontrivial (anomalous) Jacobian factor under the transformation of the path-integral measure from covariant one to canonical one.