Fluid nature constrains Horndeski gravity

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.