Locally covariant approach to effective quantum gravity

TL;DR

This paper presents a mathematically rigorous perturbative approach to effective quantum gravity using local covariance and algebraic quantum field theory, with empirical tests from cosmic microwave background measurements.

Contribution

It introduces a locally covariant framework for effective quantum gravity, combining BV-BRST formalism with algebraic QFT, enabling perturbative construction despite non-renormalisability.

Findings

Perturbation series can be constructed rigorously for quantum gravity.

Effective quantum field theory predictions are feasible at small energy scales.

Empirical tests are possible through cosmic microwave background observations.

Abstract

Despite the fact that quantum gravity is non-renormalisable, a consistent and mathematically rigorous construction of a perturbation series is possible. This is based on the use of the Batalin-Vilkovisky-Becchi-Rouet-Stora-Tyutin formalism for gauge theories, the methods of perturbative algebraic quantum field theory and the principle of local covariance. The truncation of the series can be interpreted as an effective quantum field theory which provides predictions for observations at sufficiently small energy scales. Quantum cosmology can be seen as its lowest order expansion, and precision measurements on the cosmic microwave background yield the first empirical test of this approach to quantum gravity.