2023MNRAS.520.1613R

General Relativity (GR) has been successfully tested mainly at Solar system scales; however, galaxy-scale tests have become popular in the last few decades. In this work, we investigate the η_PPN parameter, which is commonly defined by the ratio of two scalar potentials that appears in the cosmological linearly perturbed metric. Under the assumption of GR and a vanish anisotropic stress tensor, η_PPN = 1. Using ALMA, HST, and VLT/MUSE data, we combine mass measurements, using gravitational lensing and galactic dynamics, for the SDP.81 lens galaxy (z = 0.299) to constrain η_PPN. By using a flexible and self-consistent mass profile, our fiducial model takes into account the contribution of the stellar mass and a dark matter halo to reconstruct the lensed galaxy and the spatially resolved stellar kinematics. We infer, after accounting for systematic uncertainties related to the mass model, cosmology, and kinematics, $\eta _{\text{PPN}} = 1.13^{+0.03}_{-0.03}\pm 0.20\, (\text{sys})$, which is in accordance with GR predictions. Better spectroscopy data are needed to push the systematics down and bring the uncertainty to the percentage level since our analysis shows that the main source of the systematics is related to kinematics, which heavily depends on the signal-to-noise ratio of the spectra.