Gravitons in One-Loop Quantum Cosmology: Correspondence Between Covariant and Non-Covariant Formalisms

TL;DR

This paper resolves discrepancies between covariant and non-covariant one-loop calculations in quantum cosmology for higher-spin fields by analyzing perturbative quantum gravity, demonstrating their equivalence through detailed mode-by-mode analysis.

Contribution

It provides a detailed comparison and reconciliation of covariant and non-covariant formalisms in one-loop quantum gravity calculations for higher-spin fields.

Findings

One-loop amplitudes agree between covariant and non-covariant methods.

The analysis includes non-physical degrees of freedom and ghost modes.

Generalizes previous results for fermionic and electromagnetic fields.

Abstract

The discrepancy between the results of covariant and non-covariant 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 3-spheres, including non-physical 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.