## Abstract

We explore the impact of a ΛWDM cosmological scenario on the clustering properties 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 halo mass function, bias and density profiles are affected by warm dark matter (WDM). We show that, relative to cold dark matter (CDM), the halo mass function is suppressed by 50%, for masses ˜100 times the free-streaming mass scale Mfs. Consequently, the bias of low mass haloes can be boosted by as much as ˜20% for 0.25 keV WDM particles. Core densities of haloes will also be suppressed relative to the CDM case. We also examine the impact of relic thermal velocities on the density profiles, and find that these effects are constrained to scales r<1h-1kpc, 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 nonlinear matter power spectrum, and find that there is significant small-scale power in the model. However, relative to the CDM case the power is suppressed. The amount of suppression depends on the mass of the WDM particle, but can be of order 10% at k˜1hMpc-1 for particles of mass 0.25 keV. We then calculate the expected signal and noise that our set of ΛWDM 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 the Large Synoptic Survey Telescope. With Planck priors and using only multipoles l<5000, we find that a lower limit of 2.6 keV should be easily achievable.