Exploring new corners of asymptotically safe unimodular quantum gravity

TL;DR

This paper investigates the renormalization group flow of unimodular quantum gravity using polynomial truncations, finding evidence for a non-trivial fixed point compatible with the Standard Model and exploring different approximation methods.

Contribution

It introduces new fixed-point analyses of unimodular quantum gravity with various truncations and approximation schemes, including matter coupling, enhancing understanding of asymptotic safety.

Findings

Evidence for a non-trivial fixed point in unimodular quantum gravity.

Better convergence observed in the $f(R)$ truncation.

Compatibility with Standard Model matter content.

Abstract

The renormalization group flow of unimodular quantum gravity is investigated within two different classes of truncations of the flowing effective action. In particular, we search for non-trivial fixed-point solutions for polynomial expansions of the $f(R)$-type as well as of the $F(R_{\mu\nu}R^{\mu\nu})+R\,Z(R_{\mu\nu}R^{\mu\nu})$ family on a maximally symmetric background. We close the system of beta functions of the gravitational couplings with anomalous dimensions of the graviton and Faddeev-Popov ghosts treated according to two independent prescriptions: one based on the so-called background approximation and the other based on a hybrid approach which combines the background approximation with simultaneous vertex and derivative expansions. For consistency, in the background approximation, we employ a background-dependent correction to the flow equation which arises from the proper treatment of the functional measure of the unimodular path integral. We also investigate how different canonical choices of the endomorphism parameter in the regulator function affect the fixed-point structure. Although we have found evidence for the existence of a non-trivial fixed point for the two classes of polynomial projections, the $f(R)$ truncation exhibited better (apparent) convergence properties. Furthermore, we consider the inclusion of matter fields without self-interactions minimally coupled to the unimodular gravitational action and we find evidence for compatibility of asymptotically safe unimodular quantum gravity with the field content of the Standard Model and some of its common extensions.