Scientific Motivation.
In strong gravitational lensing, the image of a high-redshift source (e.g. a galaxy or a quasar) is distorted and magnified by the presence of an intervening object along the line of sight that acts as a lens (e.g. a galaxy or a galaxy cluster). The distortion is due to gravity only, allowing one to directly measure the total (i.e. luminous and dark) projected mass distribution of galaxies and galaxy clusters that act as lenses. Lensing is thus one of the most promising tools in dark matter studies, used to test different possible dark matter scenarios since we can simultaneously model the mass distribution of the main lens and its subhaloes.
The strong gravitational lensing signal by substructures is potentially in tension with CDM at both galaxy and cluster scales. In galaxy lenses, these are detected via their effect on the flux ratios of multiply imaged compact sources (Mao et al. 1988) or localised perturbations to the surface brightness distribution of magnified arcs (Koopmans 2005, Vegetti & Koopmans 2009). This method is, to this day, the only way to detect and model the presence of dark substructures beyond the Local Group, i.e. low-mass clumps that are not predicted to host a luminous component (M≤109M⦿). It has led to the detection of dark perturbers from the analysis of HST (Vegetti et al. 2010), Keck adaptive optics (Vegetti et al. 2012) and ALMA (Hezaveh et al. 2016) data: these detections are rare and thus potentially a signature of WDM models. At the same time, the detected subhaloes have an inner slope much steeper than the NFW profile (Minor et al. 2020); on top of baryonic effects, the steepening of the inner profile due to gravothermal core-collapse in velocity-dependent SIDM models could explain the observations.
The satellites of galaxy clusters and groups are instead galaxies with a clear stellar component and are included in the lens model. Also, here, the gravitational lensing signal from satellite galaxies is found to be stronger than what was predicted from CDM simulations (Meneghetti et al. 2020), pointing towards alternative dark matter models and in the same direction of galaxy-galaxy lensing The gravothermal core collapse in velocity-dependent SIDM models, combined with the baryonic contraction, is a candidate to explain the observed compact and steep profiles.
At the same time, the number of low-mass haloes and subhaloes is one of the most fundamental tests of CDM and warm dark matter models, where the number of structures should linearly increase with decreasing mass in log space.
Gravitational lensing measurements are challenging the existence of many small clumps: few have been detected, and new radio observations at milli-arcsecond resolutions are finding extremely smooth mass distributions. Any discrepancy between the observed number counts and predictions will thus be an immediate test for CDM.