Velocities as a probe of dark sector interactions

Dark energy in General Relativity is typically non-interacting with other matter. However, it is possible that the dark energy interacts with the dark matter, and in this case, the dark matter can violate the universality of free fall (the weak equivalence principle). We show that some forms of the dark sector interaction do not violate weak equivalence. For those interactions that do violate weak equivalence, there are no available laboratory experiments to probe this violation for dark matter. But cosmology provides a test for violations of the equivalence principle between dark matter and baryons – via a test for consistency of the observed galaxy velocities with the Euler equation.