Breaking the mass-sheet degeneracy in strong lensing mass modelling with weak lensing observations

The Hubble constant (H₀), a crucial parameter in cosmology, quantifies the expansion rate of the universe so its precise measurement is important to understand the fundamental dynamics of our evolving universe. One of the major limitations of measuring H₀ using time-delay cosmography is the presence of the mass-sheet degeneracy (MSD) in the lens mass modelling. We propose and quantitatively assess the use of galaxy–galaxy shear measurements to break the MSD in the strong lensing mass modelling. We use stacked galaxy–galaxy lensing profiles and corresponding covariance matrices from Huang et al. to constrain the MSD in lens mass modelling with a highly flexible mass profile. Our analyses show that if ideally all galaxy–galaxy lensing measurements from the Hyper Suprime-Cam survey can be used to constrain the MSD, we can achieve ∼ 10 per cent precision on the MSD constraint. We forecast that galaxy–galaxy lensing measurements from Legacy Survey of Space and Time (LSST)-like surveys can in general constrain the MSD with ∼ 1 per cent − 3 per cent precision. Furthermore, if we push weak lensing measurements to a lower angular scale of ∼ 0.04 Mpc, a survey like LSST can provide ∼ 1 per cent precision on the MSD constraint, enabling a measurement of H₀ at the 1 per cent level. We demonstrate that galaxy–galaxy weak lensing can robustly constrain the MSD independent of stellar kinematics of the deflector, with wide-field survey data alone.