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 ( \sim 10 ^ { 3 } Mpc ^ { 3 } ) at high magnification ( \mu \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ > $ } } 10 ) , and can detect otherwise inaccessible ultra-faint galaxies .
Even a few galaxies found in such small volumes require a very high number density of collapsed dark matter ( DM ) halos .
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 \approx 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 % ( 95 % ) confidence limit ( for a thermal relic relativistic at decoupling ) .
This limit depends only on the WDM halo mass function and , unlike previous constraints on m _ { x } , is independent of any astrophysical modeling .
The forthcoming HST Frontier Fields can significantly tighten these constraints .