The distribution of mass in galaxy-scale strong gravitational lenses is often modelled as an elliptical power law plus ‘external shear’, which notionally accounts for line-of-sight galaxies and cosmic shear. We argue that it does not, using three lines of evidence from the analysis of 54 galaxy-scale strong lenses: (i) strong lensing external shears do not correlate with weak lensing; (ii) the measured shear magnitudes in strong lenses (which are field galaxies) are too large (exceeding 0.05) for their environment and; (iii) the external shear position angle preferentially aligns or anti-aligns with the mass model position angle, indicating an internal origin. We argue the measured strong lensing shears are therefore systematically accounting for missing complexity in the canonical elliptical power-law mass model. If we can introduce this complexity into our lens models, this will further lensing studies of galaxy formation, dark matter and Cosmology.

Galaxy-galaxy strong lensing systems have been used in literature to test General Relativity by constraining the post-Newtonian parameter (γPPN). Nevertheless, these methods are prone to systematic errors, some of which arise from difficulties in modelling the dynamics of the lens galaxy. In this study, we address the systematic error related to the assumption of a constant anisotropy between the radial and tangential components of the velocity dispersion of stars within the lens galaxy, characterised by the parameter β. We considered two radial models for the anisotropy parameter, the Osipkov-Merritt and Mamon & Lokas, as well three Gaussian priors for constant β. Our analysis showed that the choice of β has a strong impact on the value of γPPN, with radial models leading to lower values of this parameter.

The gravitational lensing signal produced by a galaxy or a galaxy cluster is determined by its total matter distribution, providing us with a way to directly constrain their dark matter content. State-of-the-art numerical simulations successfully reproduce many observed properties of galaxies and can be used as a source of mock observations and predictions. Many gravitational lensing studies aim at constraining the nature of dark matter, discriminating between cold dark matter and alternative models. However, many past results are based on the comparison to simulations that did not include baryonic physics. Here we show that the presence of baryons can significantly alter the predictions: we look at the structural properties (profiles and shapes) of elliptical galaxies and at the inner density slope of subhaloes. Our results demonstrate that future simulations must model the interplay between baryons and alternative dark matter, to generate realistic predictions that could significantly modify the current constraints.

Galaxy-scale strong lensing is a powerful tool in Astrophysics and Cosmology, enabling studies of massive galaxies’ internal structure, their formation and evolution, stellar initial mass function, and cosmological parameters. In this conference proceeding, we highlight key findings from the past decade in astrophysical applications of strong lensing at the galaxy scale. We then briefly summarize the present status of discovery and analyses of new samples from recent or ongoing surveys. Finally, we offer insights into anticipated developments in the upcoming era of big data shaping the future of this field, thanks to the Rubin, Euclid, and Roman observatories.