While the direct detection of the dark-matter particle remains very challenging, the physical properties of dark matter could potentially be constrained indirectly – by comparing the population characteristics of substructures in real galaxies with predictions from the phenomenological dark-matter models, such as cold, warm or self-interacting dark matter. Whereas these models are practically indistinguishable with respect to the expected abundance and statistical properties of massive galactic substructures, the critical difference lies in the low-mass regime ≲ 108M⊙. Galaxy-galaxy strong gravitational lensing provides a unique opportunity to search for gravitational signatures of such low-mass substructures in galaxies acting as a strong gravitational lens on a more distant background galaxy, serendipitously located along the same line of sight. In [Bayer et∼al.(2023)Bayer, Chatterjee, Koopmans, Vegetti, McKean, Treu, Fassnacht, and Glazebrook, Bayer et∼al.(2023)Bayer, Koopmans, McKean, Vegetti, Treu, Fassnacht, and Glazebrook, Bayer et∼al.(2023)Bayer, Vernardos, and Koopmans], we have recently introduced a novel approach to investigate the collective perturbative effect of low-mass substructures in the inner regions of massive elliptical lens galaxies and observationally constrain their power spectrum (on 1-10 kpc scales) based on the Fourier analysis of the associated surface-brightness anomalies in the lensed images (i.e., Einstein rings and gravitational arcs) observed with the Hubble Space Telescope. Here, we present a concise summary of the methodology, the encountered modelling challenges and the inferred observational constraints on the sub-galactic matter power spectrum. The future comparison of these results with predictions from hydrodynamical simulations might either verify the cold-dark-matter paradigm or require its substantial revision. Moreover, we demonstrate that the grid-based smooth lens modelling might model away surface-brightness anomalies caused by the presence of substructures in the lens galaxy and incorrectly interpret them as surface-brightness structure in the lensed background galaxy itself. If not properly understood and accounted for, such signal suppression might lead to severely biased constraints on the properties of substructures in galactic haloes.
