Constraining sterile neutrino cosmologies with strong gravitational lensing observations at redshift z~0.2.

We use the observed amount of subhaloes and line-of-sight dark-matter haloes in a sample of eleven gravitational lens systems from the Sloan Lens ACS Survey to constrain the free-streaming properties of the dark matter particles. In particular, we combine the detection of a small-mass dark-matter halo by Vegetti et al. (2010) with the non-detections by Vegetti et al. (2014) and compare the derived subhalo and halo mass functions with expectations from Cold Dark Matter (CDM) and sterile neutrino models. We constrain the half-mode mass, i.e. the mass scale at which the linear matter power-spectrum is reduced by 50 percent relatively to the CDM model, to be $\log M_{\rm {hm}} \left[M_\odot\right] 1.02$ keV) at the 2-$\sigma$ level. This excludes sterile neutrino models with neutrino masses of $m_{\rm s} = 2.0$ keV and lepton asymmetry $L_{\rm 6} \leq 0.68$ and all values of $L_{\rm 6}$ for $m_{\rm s} < 1.5$ keV. Our constraints are weaker than currently provided by the number of Milky Way satellites, observations of the 3.5 keV X-ray line and the Lyman-$\alpha$ forest. However, they are more robust than the former as they are less affected by baryonic processes. Moreover, unlike the latter they are not affected by assumptions on the thermal histories for the inter-galactic medium. Under the assumption of a CDM dominated universe, the expected number of detectable line-of-sight haloes is $1.16\pm1.08$, in agreement with the single detection reported for this sample.