Suppressed Intrinsic Curvature Gravity

TL;DR

This paper explores modifications to gravity involving intrinsic curvature, introducing new approaches that alter gravitational wave speed and connect to Carroll gravity, with potential observational implications.

Contribution

It presents novel methods for modifying intrinsic curvature in gravity, including auxiliary fields and non-minimal scalar coupling, and analyzes their physical and cosmological consequences.

Findings

Modified gravitational wave speed compared to light

Reproduction of standard cosmological and black hole solutions

Connection to Carroll gravity as a UV completion

Abstract

We consider various mechanisms of modifying the effect of intrinsic curvature in gravity with respect to general relativity. Two primary approaches 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 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 extrinsic curvature technically natural. Although the intrinsic curvature and its modification may depend on the foliation, we use the covariant formalism and show that such a foliation always exists. Perhaps the most important outcome is that in the non-minimal coupling approach, the intrinsic curvature appearing in Einstein's field equations can defer from the one appearing in the geodesic equation potentially leading to important observational consequences.