Nonderivative Modified Gravity: a Classification

TL;DR

This paper classifies modified gravity theories with nonderivative potentials based on their degrees of freedom, revealing which configurations are viable, strongly coupled, or equivalent to a cosmological constant, with implications for cosmology.

Contribution

It provides a nonperturbative classification of nonderivative modified gravity potentials according to their propagating degrees of freedom, extending previous perturbative analyses.

Findings

Generic potentials propagate 6 DoF with a ghost on Minkowski background.

Potentials with 5 DoF have been studied previously and are viable.

Potentials with 2 DoF correspond to massive gravitons and act as a cosmological constant.

Abstract

We analyze the theories of gravity modified by a generic nonderivative potential built from the metric, under the minimal requirement of unbroken spatial rotations. Using the canonical analysis, we classify the potentials $V$ according to the number of degrees of freedom (DoF) that propagate at the nonperturbative level. We then compare the nonperturbative results with the perturbative DoF propagating around Minkowski and FRW backgrounds. A generic $V$ implies 6 propagating DoF at the non-perturbative level, with a ghost on Minkowski background. There exist potentials which propagate 5 DoF, as already studied in previous works. Here, no $V$ with unbroken rotational invariance admitting 4 DoF is found. Theories with 3 DoF turn out to be strongly coupled on Minkowski background. Finally, potentials with only the 2 DoF of a massive graviton exist. Their effect on cosmology is simply equivalent to a cosmological constant. Potentials with 2 or 5 DoF and explicit time dependence appear to be a further viable possibility.