Suppressed Intrinsic Curvature Gravity

Abstract

We consider various mechanisms of modifying the effect of intrinsic curvature in gravity with respect to General Relativity. Two primary approaches for suppressing intrinsic curvature are studied. First, by considering a Lagrange multiplier or an auxiliary field. Second, by non-minimal coupling between a scalar field and the intrinsic curvature scalar. We promote the foliation to a dynamical field, getting a fully covariant, and foliation independent theory. We reproduce the basic solutions of FLRW cosmology, black hole solutions, Lense-Thirring effect, and gravitational waves. The speed of gravitational waves is modified in comparison to the speed of light. A certain limit of our theory corresponds to the lowest-order Carroll gravity. Hence, our theory is a different UV completion of Carroll gravity, compared to the usual expansion of a small speed of light. Carroll gravity limit also has an enhanced symmetry, making the reduced or vanishing intrinsic curvature technically natural. Finally, our construction defines a one parameter family of theories, that sets the relative strength of the intrinsic and extrinsic curvature, and General Relativity corresponds to a specific value of this parameter.