Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm

Horndeski gravity is a popular contender for a phenomenological model of dy-namical 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.

Automated summary

In this study, we investigate whether Horndeski gravity can be more than just a phenomenological model and become a fundamental theory incorporating quantum effects at high energy scales. We find that within the asymptotic-safety paradigm, it is possible to achieve an ultraviolet completion of a certain class of Horndeski gravity models. However, the couplings required by these models are incompatible with dynamical dark energy. Similarly, under the assumption of no new strongly-coupled physics below the Planck scale, quantum gravity fluctuations limit the Horndeski couplings, making it difficult to explain dynamical dark energy.