Future constraints on the gravitational slip with the mass profiles of galaxy clusters

The gravitational slip parameter, defined as the ratio between the two scalar potentials appearing in the linearly perturbed Friedmann-Lemaitre-Robertson Walker metric, is an important discriminator between large classes of gravity theories at cosmological and astrophysical scales. In this work we use a combination of simulated information of galaxy cluster mass profiles, inferred by strong + weak lensing analyses and by the study of the dynamics of the cluster member galaxies, to reconstruct the gravitational slip parameter η and predict the accuracy with which it can be constrained with current and future galaxy cluster surveys. Performing a full-likelihood statistical analysis, we show that galaxy cluster observations can constrain η down to per cent level already with a few tens of clusters. We discuss the significance of possible systematics, and show that the clusters masses and numbers of galaxy members used to reconstruct the dynamics mass profile have a mild effect on the predicted constraints.