  A defining prediction of the cold dark matter (CDM) cosmological model is the
existence of a very large population of low-mass haloes. This population is
absent in models in which the dark matter particle is warm (WDM). These
alternatives can, in principle, be distinguished observationally because halos
along the line-of-sight can perturb galaxy-galaxy strong gravitational lenses.
Furthermore, the WDM particle mass could be deduced because the cut-off in
their halo mass function depends on the mass of the particle. We systematically
explore the detectability of low-mass haloes in WDM models by simulating and
fitting mock lensed images. Contrary to previous studies, we find that halos
are harder to detect when they are either behind or in front of the lens.
Furthermore, we find that the perturbing effect of haloes increases with their
concentration: detectable haloes are systematically high-concentration haloes,
and accounting for the scatter in the mass-concentration relation boosts the
expected number of detections by as much as an order of magnitude. Haloes have
lower concentration for lower particle masses and this further suppresses the
number of detectable haloes beyond the reduction arising from the lower halo
abundances alone. Taking these effects into account can make lensing
constraints on the value of the mass function cut-off at least an order of
magnitude more stringent than previously appreciated.
