Testing the Equivalence Principle in Galaxy Clusters

Clusters of galaxies have been used to measure a subtle effect predicted by Einstein: gravitational redshift. This signal encodes pristine information about our Universe, since it is sensitive to the depth of the clusters'gravitational potential wells. In this work, we show how gravitational redshift can be used to test a fundamental physical principle: the weak equivalence principle. This principle stipulates that all matter falls in the same way in a gravitational potential, regardless of its nature. By comparing the amplitude of the gravitational redshift signal with the velocity dispersion in galaxy clusters, we build a novel test of this principle targeted to the unknown dark matter. Our test is sensitive to any additional interaction that would alter the way dark matter falls in gravitational potentials, hence leading to a violation of the equivalence principle. We show that currently available data can constrain the presence of a fifth force in clusters at the level of 7-14%, while the newest surveys will reach a precision of a few percents. This demonstrates the crucial role played by galaxy clusters in testing fundamental properties of dark matter.