SHARP -- VII. New constraints on warm dark matter free-streaming properties and substructure abundance from flux-ratio anomalous lensed quasars.

We present an analysis of seven strongly gravitationally lensed quasars and the corresponding constraints on the properties of dark matter. Our results are derived by modelling the lensed image positions and flux-ratios using a combination of smooth macro models and a population of low-mass haloes within the mass range $10^6$ to $10^9$ M$_\odot$. Our lens models explicitly include higher-order complexity in the form of stellar discs and luminous satellites, and low-mass haloes located along the observed lines of sight for the first time. Assuming a Cold Dark Matter (CDM) cosmology, we infer an average total mass fraction in substructure of $f_{\rm sub} = 0.011^{+0.007}_{-0.005}$ (68 per cent confidence limits), which is in agreement with the predictions from CDM hydrodynamical simulations to within 1$\sigma$. This result is significantly different when compared to previous studies that did not include line-of-sight haloes. Under the assumption of a thermal relic warm dark matter (WDM) model, we derive a lower limit on the particle relic mass of $m_{\rm wdm} > 2.93$ keV (95 per cent confidence limits), which is consistent with a value of $m_{\rm wdm} > 3.5$ keV from the recent analysis of the Ly$\alpha$ forest.