Asymptotically safe gravity as a scalar-tensor theory and its cosmological implications

TL;DR

This paper explores asymptotically safe gravity through a scalar-tensor framework, examining its cosmological implications, inflationary solutions, and the effects of a running gravitational constant on cosmological perturbations.

Contribution

It demonstrates the equivalence of asymptotically safe gravity to a specific scalar-tensor theory and discusses its reformulation as an $f(R)$ model, including cosmological solutions and perturbation effects.

Findings

Classical behavior matches a Jordan-Brans-Dicke theory with zero Brans-Dicke parameter.

Identifies large-field inflationary solutions near the Planck scale.

Highlights the importance of the running gravitational constant in cosmological perturbations.

Abstract

We study asymptotically safe gravity with Einstein-Hilbert truncation taking into account the renormalization group running of both gravitational and cosmological constants. We show the classical behavior of the theory is equivalent to a specific class of Jordan-Brans-Dicke theories with vanishing Brans-Dicke parameter, and potential determined by the renormalization group equation. The theory may be reformulated as an $f(R)$ theory. In the simplest cosmological scenario, we find large--field inflationary solutions near the Planck scale where the effective field theory description breaks down. Finally, we discuss the implications of a running gravitational constant to background dynamics via cosmological perturbation theory. We show that compatibility with General Relativity requires contributions from the running gravitational constant to the stress energy tensor to be taken into account in the perturbation analysis.