Focusing on warm dark matter with lensed high-redshift galaxies

We propose a novel use of high-redshift galaxies, discovered in deep Hubble Space Telescope (HST) fields around strong lensing clusters. These fields probe small comoving volumes (similar to 10(3) Mpc(3)) at high magnification (mu greater than or similar to 10) and can detect otherwise inaccessible ultrafaint galaxies. Even a few galaxies found in such small volumes require a very high number density of collapsed dark matter (DM) haloes. This implies significant primordial power on small scales, allowing these observations to rule out popular alternatives to standard cold dark matter (CDM) models, such as warm dark matter (WDM). In this work, we analytically compute WDM halo mass functions at z = 10, including the effects of both particle free-streaming and residual velocity dispersion. We show that the two z approximate to 10 galaxies already detected by the Cluster Lensing And Supernova survey with Hubble (CLASH) survey are sufficient to constrain the WDM particle mass to m(x) > 1 (0.9) keV at 68 per cent (95 per cent) confidence limit (for a thermal relic relativistic at decoupling). This limit depends only on the WDM halo mass function and, unlike previous constraints on mx, is independent of any astrophysical modelling. The forthcoming HST Frontier Fields can significantly tighten these constraints.