CLASH-VLT: Constraining deviation from GR with the mass profiles of nine massive galaxy clusters

We investigate the anisotropic stress parameter, η = Ψ/Φ, defined as the ratio of the gravitational potentials in the linearly perturbed Friedmann-Lemaître Robertson-Walker metric, as a probe of deviations from general relativity across astrophysical to cosmological scales. Using mass profiles reconstructed from high-precision lensing and kinematics of nine galaxy clusters from the CLASH-VLT sample, we derive η(r) as a function of the radial distance from the cluster centres, over the range [0.1 Mpc,1.2 r200L], where r200L is virial radius best-fit from lensing data. When using a Navarro-Frenk-White or an Hernquist profile to model the total matter distribution, we find consistency with general relativity (η = 1) within 2σ for the full radial range for all the sampled clusters. However, adopting a Burkert profile introduces mild tension with general relativity, reaching the 3σ level in two systems. Assuming a negligible time-dependence in the redshift range spawned by the clusters, we obtain the joint constraint η (η = 1.0 Mpc) = 0.93+0.48-0.40 (stat) ± 0.47 (syst) at 95% confidence level — an improvement of approximately 40% over previous estimates. We discuss the impact of systematics on the constraints, and we highlight the implications of this result for current and upcoming cluster surveys.