Nonderivative Modified Gravity: a Classification

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.

No comment

References in corpus (9)

• Resummation of Massive Gravity
• Infrared-modified gravities and massive gravitons
• Improved constraints on non-Newtonian forces at 10 microns
• Acausality of Massive Gravity
• Spontaneous Lorentz Breaking and Massive Gravity
• Lorentz Breaking Massive Gravity in Curved Space
• Degrees of Freedom in Massive Gravity
• FRW Cosmological Perturbations in Massive Bigravity
• Cosmology in rotation-invariant massive gravity with non-trivial fiducial metric

Cited by in corpus (2)

• Massive gravity and the suppression of anisotropies and gravitational waves in a matter-dominated contracting universe
• New Branches of Massive Gravity