Background Independence and Asymptotic Safety in Conformally Reduced Gravity

TL;DR

This paper explores how background independence affects the renormalization group flow in quantum gravity, demonstrating that it can lead to the existence of a non-Gaussian fixed point essential for asymptotic safety, especially in conformally reduced models.

Contribution

It shows that background independence introduces an extra field dependence in the RG flow, which can reveal fixed points not seen in standard approaches, advancing understanding of asymptotic safety in quantum gravity.

Findings

Background independence alters the RG flow significantly.

A non-Gaussian fixed point exists in the background independent flow.

The conformally reduced model reproduces key features of full Einstein-Hilbert truncation.

Abstract

We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG flow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a non-Gaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of Quantum Einstein Gravity in the ``conformally reduced'' Einstein--Hilbert approximation which discards all degrees of freedom contained in the metric except the conformal one. Without the extra field dependence the resulting RG flow is that of a simple $\phi^4$-theory. Including it one obtains a flow with exactly the same qualitative properties as in the full Einstein--Hilbert truncation. In particular it possesses the non-Gaussian fixed point which is necessary for asymptotic safety.