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Abstract 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 r 200 L , where r 200 L 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.
Pizzuti et al. (Sun,) studied this question.