On the Vilkovisky-DeWitt approach and renormalization group in effective quantum gravity

TL;DR

This paper discusses how the Vilkovisky-DeWitt effective action approach enables a gauge-invariant and parametrization-independent analysis of the renormalization group flow in quantum gravity, focusing on the running of fundamental constants.

Contribution

It demonstrates that the Vilkovisky-DeWitt effective action allows for a consistent, gauge-independent renormalization group analysis in quantum gravity, with one-loop beta functions regarded as exact.

Findings

One-loop beta functions are considered exact and free from higher-loop corrections.

The approach enables exploration of the running of the cosmological and Newton constants.

The renormalization group flow connects the IR Hubble scale to the UV Planck scale.

Abstract

The effective action in quantum general relativity is strongly dependent on the gauge-fixing and parametrization of the quantum metric. As a consequence, in the effective approach to quantum gravity, there is no possibility to introduce the renormalization-group framework in a consistent way. On the other hand, the version of effective action proposed by Vilkovisky and DeWitt does not depend on the gauge-fixing and parametrization off-shell, opening the way to explore the running of the cosmological and Newton constants as well as the coefficients of the higher-derivative terms of the total action. We argue that in the effective framework the one-loop beta functions for the zero-, two- and four-derivative terms can be regarded as exact, that means, free from corrections coming from the higher loops. In this perspective, the running describes the renormalization group flow between the present-day Hubble scale in the IR and the Planck scale in the UV.