Stability of a black hole and the speed of gravity waves within self-tuning cosmological models

TL;DR

This paper demonstrates that certain beyond-Horndeski theories can ensure the speed of gravity matches light speed near black holes and in the cosmological background, while also providing a self-tuning mechanism for the cosmological constant.

Contribution

It shows that imposing gravity-light speed equality in specific theories guarantees this equality near black holes and supports a self-tuning solution for the cosmological constant.

Findings

Speed of gravity equals light speed near black holes in these models.

The solutions are stable within certain parameter ranges.

The models can self-tune the cosmological constant to a small value.

Abstract

The gravitational wave event GW170817 together with its electromagnetic counterparts constrains the speed of gravity to be extremely close to that of light. We first show, on the example of an exact Schwarzschild-de Sitter solution of a specific beyond-Horndeski theory, that imposing the strict equality of these speeds in the asymptotic homogeneous Universe suffices to guarantee so even in the vicinity of the black hole, where large curvature and scalar-field gradients are present. We also find that the solution is stable in a range of the model parameters. We finally show that an infinite class of beyond-Horndeski models satisfying the equality of gravity and light speeds still provide an elegant self-tuning: The very large bare cosmological constant entering the Lagrangian is almost perfectly counterbalanced by the energy-momentum tensor of the scalar field, yielding a tiny observable effective cosmological constant.