Probing a scale dependent gravitational slip with galaxy strong lensing systems

Abstract

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

12 pages, 5 figures

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