Gravitons in one-loop quantum cosmology: correspondence between covariant and noncovariant formalisms

The discrepancy between the results of covariant and noncovariant one-loop calculations for higher-spin fields in quantum cosmology is analyzed. A detailed mode-by-mode study of perturbative quantum gravity about a flat Euclidean background bounded by two concentric three-spheres, including nonphysical degrees of freedom and ghost modes, leads to one-loop amplitudes in agreement with the covariant Schwinger-DeWitt method. This calculation provides the generalization of a previous analysis of fermionic fields and electromagnetic fields at one-loop about flat Euclidean backgrounds admitting a well-defined 3+1 decomposition.