Time-delay distance measurements of strongly lensed quasars have provided a powerful and independent probe of the current expansion rate of the Universe (H 0 ). However, in light of the discrepancies between early and late-time cosmological studies, current efforts revolve around the characterisation of systematic uncertainties in the methods. In this work, we focus on the mass-sheet degeneracy (MSD), which is commonly considered as being a significant source of systematics in time-delay strong lensing studies, and aim to assess the constraining power provided by integral field unit (IFU) stellar kinematics. To this end, we approximate the MSD with a cored, two-parameter extension to the adopted lensing mass profiles (with core radius r c and mass-sheet parameter λ int ), which introduces a full degeneracy between λ int and H 0 from lensing data alone. In addition, we utilise spatially resolved mock IFU stellar kinematics of time-delay strong lenses, given the prospects of obtaining such high-quality data with the James Webb Space Telescope (JWST) in the near future. We construct joint strong lensing and generalised two-integral axisymmetric Jeans models, where the time delays, mock imaging and IFU observations are used as input to constrain the mass profile of lens galaxies at the individual galaxy level, and consequently yield joint constraints on the time-delay distance (D ∆t ) and angular diameter distance (D d ) to the lens. We find that mock JWST-like stellar kinematics constrain the amount of internal mass sheet that is physically associated with the lens galaxy and limit its contribution to the uncertainties of D ∆t and D d , each at the ≤ 4% level, without assumptions on the background cosmological model. Incorporating additional uncertainties due to external mass sheets associated with mass structures along the lens line-of-sight, these distance constraints would translate to a 4% precision measurement on H 0 in flat ΛCDM cosmology for a single lens. Our study shows that future IFU stellar kinematics of time-delay lenses will be key in lifting the MSD on a per lens basis, assuming reasonable and physically motivated core sizes. However, even in the limit of infinite r c , where D ∆t is fully degenerate with λ int and is thus not constrained, stellar kinematics of the deflector, time delays and imaging data will provide powerful constraints on D d , which becomes the dominant source of information in the cosmological inference.

Time-delay distance measurements of strongly lensed quasars have provided a powerful and independent probe of the current expansion rate of the Universe (H0). However, in light of the discrepancies between early- and late-time cosmological studies, current efforts revolve around the characterisation of systematic uncertainties in the methods. In this work we focus on the mass-sheet degeneracy (MSD), which is commonly considered a significant source of systematics in time-delay strong lensing studies, and aim to assess the constraining power provided by integral field unit (IFU) stellar kinematics. To this end, we approximated the MSD with a cored, two-parameter extension to the adopted lensing mass profiles (with core radius rc and mass-sheet parameter λint), which introduces a full degeneracy between λint and H0 from lensing data alone. In addition, we utilised spatially resolved mock IFU stellar kinematics of time-delay strong lenses, given the prospects of obtaining such high-quality data with the James Webb Space Telescope (JWST) in the near future. We constructed joint strong lensing and generalised two-integral axisymmetric Jeans models, where the time delays, mock imaging, and IFU observations are used as input to constrain the mass profile of lens galaxies at the individual galaxy level and consequently yield joint constraints on the time-delay distance (DΔt) and the angular diameter distance (Dd) to the lens. We find that mock JWST-like stellar kinematics constrain the amount of internal mass sheet that is physically associated with the lens galaxy and limit its contribution to the uncertainties of DΔt and Dd, each at the ≤4% level, without assumptions on the background cosmological model. Incorporating additional uncertainties due to external mass sheets associated with mass structures along the lens line of sight, these distance constraints would translate to a ≲4% precision measurement on H0 in flat Λ cold dark matter cosmology for a single lens. Our study shows that future IFU stellar kinematics of time-delay lenses will be key in lifting the MSD on a per lens basis, assuming reasonable and physically motivated core sizes. However, even in the limit of infinite rc, where DΔt is fully degenerate with λint and is thus not constrained, stellar kinematics of the deflector, time delays, and imaging data will provide powerful constraints on Dd, which becomes the dominant source of information in the cosmological inference.