Probing a scale dependent gravitational slip with galaxy strong lensing systems

Observations of galaxy-scale strong gravitational lensing systems enable unique tests of departures from general relativity at the kpc-Mpc scale. In this work, the gravitational slip parameter ${\gamma }_{\mathrm{P}\mathrm{N}}$, measuring the amplitude of a hypothetical fifth force, is constrained using 130 elliptical galaxy lens systems. We implement a lens model with a power-law total mass density and a deprojected De Vaucouleurs luminosity density, favored over a power-law luminosity density. To break the degeneracy between the lens velocity anisotropy, $\beta$, and the gravitational slip, we introduce a new prior on the velocity anisotropy based on recent dynamical data. For a constant gravitational slip, we find ${\gamma }_{\mathrm{P}\mathrm{N}}=0.90_{-0.14}^{+0.18}$ in agreement with general relativity at the 68% confidence level. Introducing a Compton wavelength ${\lambda }_g$, effectively screening the fifth force at small and large scales, the best fit is obtained for ${\lambda }_g\sim 0.2$ Mpc and ${\gamma }_{\mathrm{P}\mathrm{N}}=0.77_{-0.14}^{+0.25}$. A local minimum is found at ${\lambda }_g\sim 100$ Mpc and ${\gamma }_{\mathrm{P}\mathrm{N}}=0.56_{-0.35}^{0.45}$. We conclude that there is no evidence in the data for a significant departure from general relativity and that using accurate assumptions and having good constraints on the lens galaxy model is key to ensure reliable constraints on the gravitational slip.