"Testing the equivalence principle in the dark sector"
The equivalence between the inertial and gravitational mass is built-in the formulation of General Relativity as the curvature of space time. In the visible sector, the equivalence principle has been tested with extraordinary precision, but very little is known about the presence of long range fifth forces in the dark sector. In this talk I will describe how we can use cosmological data to test whether dark matter violates the equivalence principle. The Universe itself will act as a scale that measures if dark matter particles fall in the same way as ordinary particles. After discussing the main effects of dark fifth forces on cosmological observables like the CMB and matter power spectrum, I will present the constraints on the strength of the new interaction using Planck and BAO data. Our results indicate that equivalence principle violations in the dark sector are at most a few parts in one thousand, which is the best available bound on such new forces. Interestingly, a violation of the equivalence principle in the dark sector can alleviate the strong tension between local and CMB estimate of the Hubble constant.