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 $\gamma_{\rm PN}$, 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 $\gamma_{\rm PN}=0.90^{+0.18}_{-0.14}$ 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 $\gamma_{\rm PN} = 0.77^{+0.25}_{-0.14}$. A local minimum is found at $\lambda_g \sim 100$ Mpc and $\gamma_{\rm PN}=0.56^{0.45}_{-0.35}$. 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.