Gravitational alternatives to dark matter with tensor mode speed equaling the speed of light

A number of theories of gravity have been proposed as proxies for dark matter in the regime of galaxies and cosmology. The recent observations of gravitational waves (GW170817) from the merger of two neutron stars, followed by an electromagnetic counterpart (GRB170817a) have placed stringent constraints on the difference between the speeds of gravity and light, severely restricting the phenomenological viability of such theories. We revisit the impact of these observations on the tensor-vector-scalar paradigm of relativistic modified Newtonian dynamics (MOND) and demonstrate the existence of a previously unknown class of this paradigm where the speed of gravity always equals the speed of light. We show that this holds without altering the usual (bimetric) MOND phenomenology in galaxies.