Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm

TL;DR

This paper investigates whether Horndeski gravity can be a fundamental quantum theory within the asymptotic-safety paradigm, finding that quantum constraints prevent it from explaining dynamical dark energy.

Contribution

It demonstrates that asymptotic safety imposes strong coupling constraints on Horndeski gravity, limiting its role as a fundamental theory for dark energy.

Findings

Ultraviolet completion of Horndeski is possible but constrains couplings.

Quantum effects prevent Horndeski from explaining dark energy.

Constraints are incompatible with dynamical dark energy.

Abstract

Horndeski gravity is a popular contender for a phenomenological model of dynamical dark energy, and as such subject to observational constraints. In this work, we ask whether Horndeski gravity can be more than a phenomenological model and instead become a fundamental theory, which extends towards high energy scales and includes quantum effects. We find that within the asymptotic-safety paradigm, an ultraviolet completion of a simple class of models of Horndeski gravity is achievable, but places strong constraints on the couplings of the theory. These constraints are not compatible with dynamical dark energy. Further, we find a similar result in an effective-field theory approach to this class of models of Horndeski gravity: under the assumption that there is no new strongly-coupled physics below the Planck scale, quantum gravity fluctuations force the Horndeski couplings to be too small to achieve an explanation of dynamical dark energy.