Matter in the beam: Weak lensing, substructures and the temperature of
  dark matter
  Warm Dark Matter (WDM) models offer an attractive alternative to the current
Cold Dark Matter (CDM) cosmological model. We present a novel method to
differentiate between WDM and CDM cosmologies, namely using weak lensing; this
provides a unique probe as it is sensitive to all the "matter in the beam", not
just dark matter haloes and the galaxies that reside in them, but also the
diffuse material between haloes. We compare the weak lensing maps of CDM
clusters to those in a WDM model corresponding to a thermally produced
$0.5$~keV dark matter particle. Our analysis clearly shows that the weak
lensing magnification, convergence and shear distributions can be used to
distinguish between CDM and WDM models. WDM models {\em increase} the
probability of weak magnifications, with the differences being significant to
$\gtrsim5\sigma$, while leaving no significant imprint on the shear
distribution. WDM clusters analysed in this work are more homogeneous than CDM
ones, and the fractional decrease in the amount of material in haloes is
proportional to the average increase in the magnification. This difference
arises from matter that would be bound in compact haloes in CDM being smoothly
distributed over much larger volumes at lower densities in WDM. Moreover, the
signature does not solely lie in the probability distribution function but in
the full spatial distribution of the convergence field.
