Essential Quantum Einstein Gravity

TL;DR

This paper investigates the non-perturbative renormalisation of quantum gravity, identifying a universal, unitary class where Newton's constant is the sole essential coupling, supporting the asymptotic safety scenario with no free parameters.

Contribution

It introduces a reparameterisation approach along the RG flow to focus on essential couplings, demonstrating the stability of the Reuter fixed point and the dominance of Newton's constant in quantum Einstein gravity.

Findings

Newton's constant is the only essential coupling at the Reuter fixed point.

The Reuter fixed point properties are stable under inclusion of four-derivative terms.

Quantum Einstein gravity likely has no free parameters and predicts a vanishing cosmological constant.

Abstract

The non-perturbative renormalisation of quantum gravity is investigated allowing for the metric to be reparameterised along the RG flow, such that only the essential couplings constants are renormalised. This allows us to identify a universality class of quantum gravity which is guaranteed to be unitary, since the physical degrees of freedom are those of general relativity without matter and with a vanishing cosmological constant. Considering all diffeomorphism invariant operators with up to four derivatives, only Newton's constant is essential at the Gaussian infrared fixed point associated to the linearised Einstein--Hilbert action. The other inessential couplings can then be fixed to the values they take at the Gaussian fixed point along the RG flow within this universality class. In the ultraviolet, the corresponding beta function for Newton's constant vanishes at the interacting Reuter fixed point. The properties of the Reuter fixed point are stable between the Einstein--Hilbert approximation and the approximation including all diffeomorphism invariant four derivative terms in the flow equation. Our results suggest that Newton's constant is the only relevant essential coupling at the Reuter fixed point. Therefore, we conjecture that quantum Einstein gravity, the ultraviolet completion of Einstein's theory of general relativity in the asymptotic safety scenario, has no free parameters in the absence of matter and in particular predicts a vanishing cosmological constant.