  We explore the impact of a LWDM cosmological scenario on the clustering
properties of large-scale structure in the Universe. We do this by extending
the halo model. The new development is that we consider two components to the
mass density: one arising from mass in collapsed haloes, and the second from a
smooth component of uncollapsed mass. Assuming that the nonlinear clustering of
dark matter haloes can be understood, then from conservation arguments one can
precisely calculate the clustering properties of the smooth component and its
cross-correlation with haloes. We then explore how the three main ingredients
of the halo calculations, the mass function, bias and density profiles are
affected by WDM. We show that, relative to CDM: the mass function is suppressed
by ~50%, for masses ~100 times the free-streaming mass-scale; the bias of low
mass haloes can be boosted by up to 20%; core densities of haloes can be
suppressed. We also examine the impact of relic thermal velocities on the
density profiles, and find that these effects are constrained to scales r<1
kpc/h, and hence of little importance for dark matter tests, owing to
uncertainties in the baryonic physics. We use our modified halo model to
calculate the non-linear matter power spectrum, and find significant
small-scale power in the model. However, relative to the CDM case, the power is
suppressed. We then calculate the expected signal and noise that our set of
LWDM models would give for a future weak lensing mission. We show that the
models should in principle be separable at high significance. Finally, using
the Fisher matrix formalism we forecast the limit on the WDM particle mass for
a future full-sky weak lensing mission like Euclid or LSST. With Planck priors
and using multipoles l<5000, we find that a lower limit of 2.6 keV should be
easily achievable.
