The first simultaneous measurement of Hubble constant and post-Newtonian parameter from time-delay strong lensing

Strong gravitational lensing has been a powerful probe of cosmological models and gravity. To date, constraints in either domain have been obtained separately. We propose a new methodology through which the cosmological model, specifically the Hubble constant, and post-Newtonian parameter can be simultaneously constrained. Using the time-delay cosmography from strong lensing combined with the stellar kinematics of the deflector lens, we demonstrate that the Hubble constant and post-Newtonian parameter are incorporated in two distance ratios that reflect the lensing mass and dynamical mass, respectively. Through the re-analysis of the four publicly released lenses distance posteriors from the H0LiCOW (H0 Lenses in COSMOGRAIL's Wellspring) collaboration, the simultaneous constraints of Hubble constant and post-Newtonian parameter are obtained. Our results suggest no deviation from the general relativity; γ_PPN = 0.87⁺₋⁰₀¹⁹₁₇ with a Hubble constant that favours the local Universe value, H₀ = 73.65⁺₋¹₂⁹⁵₂₆ km s⁻¹ Mpc⁻¹. Finally, we forecast the robustness of gravity tests by using the time-delay strong lensing for constraints we expect in the next few years. We find that the joint constraint from 40 lenses is able to reach the order of 7.7 per cent for the post-Newtonian parameter and 1.4 per cent for the Hubble constant.