Fluid nature constrains Horndeski gravity

TL;DR

This paper models Horndeski gravity as a dissipative fluid, revealing that only Newtonian-like effective fluids within this class allow gravitational waves to travel at light speed, thus constraining the theory's physical nature.

Contribution

It introduces a fluid-based approach to Horndeski gravity, identifying conditions under which gravitational waves propagate at light speed and classifying viable theories accordingly.

Findings

Only two subclasses of Horndeski gravity are consistent with Newtonian fluid behavior.

Gravitational wave speed equals light speed if the effective fluid's stress-energy tensor is linear in velocity derivatives.

Most Horndeski theories correspond to non-Newtonian, exotic fluid behaviors.

Abstract

The elusive physical nature of Horndeski gravity is elucidated in a new approach depicting this class of theories as a dissipative effective fluid. Requiring the constitutive equations of the latter to be those of a Newtonian fluid restricts the theory to only two disconnected subclasses of "viable" Horndeski gravity. Therefore, a stress-energy tensor of Horndeski effective fluid, linear in the first derivatives of the fluid's 4-velocity, is a sufficient condition for gravitational waves to propagate at light speed. All other Horndeski theories correspond to exotic non-Newtonian effective fluids.