Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case

TL;DR

This paper investigates the existence and properties of non-Gaussian fixed points in f(R)-gravity coupled to matter, using the functional renormalization group, to assess the asymptotic safety of gravity-matter systems including the Standard Model.

Contribution

It provides a detailed analysis of NGFPs in f(R)-gravity with matter, employing a flexible coarse-graining scheme and clarifies the universality classes of fixed points in different regularization settings.

Findings

Gravity coupled to Standard Model matter exhibits NGFPs similar to pure gravity.

Inclusion of higher powers of scalar curvature improves fixed point properties.

Different coarse-graining operators lead to different universality classes of NGFPs.

Abstract

We use the functional renormalization group equation for the effective average action to study the non-Gaussian renormalization group fixed points (NGFPs) arising within the framework of f(R)-gravity minimally coupled to an arbitrary number of scalar, Dirac, and vector fields. Based on this setting we provide comprehensible estimates which gravity-matter systems give rise to NGFPs suitable for rendering the theory asymptotically safe. The analysis employs an exponential split of the metric fluctuations and retains a 7-parameter family of coarse-graining operators allowing the inclusion of non-trivial endomorphisms in the regularization procedure. For vanishing endomorphisms, it is established that gravity coupled to the matter content of the standard model of particle physics and many beyond the standard model extensions exhibit NGFPs whose properties are strikingly similar to the case of pure gravity: there are two UV-relevant directions and the position and critical exponents converge rapidly when higher powers of the scalar curvature are included. Conversely, none of the phenomenologically interesting gravity-matter systems exhibits a stable NGFP when a Type II coarse graining operator is employed. Our analysis resolves this tension by demonstrating that the NGFPs seen in the two settings belong to different universality classes.