Background-metric Independent Formulation of 4D Quantum Gravity

TL;DR

This paper develops a background-metric independent formulation of 4D quantum gravity, emphasizing the importance of 4th order derivatives and analyzing the model in the limit where the self-coupling constant approaches zero.

Contribution

It introduces a novel background-metric independent approach to 4D quantum gravity, focusing on the measure and action with 4 derivatives, and studies the model in the t→0 limit.

Findings

Exact evaluation of the measure at t→0 limit

Perturbative determination of t-dependence of the measure

Highlights the role of 4th order gravity in quantum gravity formulation

Abstract

Using the background-metric independence for the traceless mode as well as the conformal mode, 4D quantum gravity is described as a quantum field theory defined on a non-dynamical background-metric. The measure then induces an action with 4 derivatives. So we think that 4-th order gravity is essential and the Einstein-Hilbert term should be treated like a mass term. We introduce the dimensionless self-coupling constant t for the traceless mode. In this paper we study a model where the measure can be evaluated in the limit $t \to 0$ exactly, using the background-metric independence for the conformal mode. The t-dependence of the measure is determined perturbatively using the background-metric independence for the traceless mode.