Search of scaling solutions in scalar-tensor gravity

TL;DR

This paper develops simplified functional renormalization group equations for scalar-tensor gravity, identifying potential fixed points that could inform quantum gravity theories in various dimensions.

Contribution

It introduces new, simplified RG equations for scalar-tensor gravity that reveal possible fixed points, including a gravitationally dressed Wilson-Fisher fixed point.

Findings

Existence of a gravitationally dressed Wilson-Fisher fixed point in three dimensions.

Identification of two analytic scaling solutions for dimensions greater than two.

One solution aligns with the Einstein-Hilbert fixed point, the other involves non-zero minimal coupling.

Abstract

We write new functional renormalization group equations for a scalar nonminimally coupled to gravity. Thanks to the choice of the parametrization and of the gauge fixing they are simpler than older equations and avoid some of the difficulties that were previously present. In three dimensions these equations admit, at least for sufficiently small fields, a solution that may be interpreted as a gravitationally dressed Wilson-Fisher fixed point. We also find for any dimension d>2 two analytic scaling solutions which we study for d=3 and d=4. One of them corresponds to the fixed point of the Einstein-Hilbert truncation, the others involve a nonvanishing minimal coupling.