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We use state-of-art measurements of the galaxy luminosity function (LF) atz=6, 7 and 8 to derive constraints on warm dark matter (WDM), late-forming darkmatter (LFDM) and ultra-light axion dark matter (ULADM) models alternative tothe cold dark matter (CDM) paradigm. To this purpose we have run a suite ofhigh-resolution N-body simulations to accurately characterise the low mass-endof the halo mass function and derive DM model predictions of the high-zluminosity function. In order to convert halo masses into UV-magnitudes weintroduce an empirical approach based on halo abundance matching which allowsus to model the LF in terms of the amplitude and scatter of the ensembleaverage star formation rate halo mass relation of each DM model, $\langle {\rmSFR}({\rm M_{ h}},z)\rangle$. We find that independent of the DM scenario theaverage SFR at fixed halo mass increases from z=6 to 8, while the scatterremains constant. At halo mass ${\rm M_{h}}\gtrsim 10^{12}\,{\rm M}_\odot$h$^{-1}$ the average SFR as function of halo mass follows a double power lawtrend that is common to all models, while differences occur at smaller masses.In particular, we find that models with a suppressed low-mass halo abundanceexhibit higher SFR compared to the CDM results. Using deviance statistics weobtain a lower limit on the WDM thermal relic particle mass, $m_{\rmWDM}\gtrsim 1.5$ keV at $2\sigma$. In the case of LFDM models, the phasetransition redshift parameter is bounded to $z_t\gtrsim 8\cdot 10^5$ at$2\sigma$. We find ULADM best-fit models with axion mass $m_a\gtrsim 1.6\cdot10^{-22}$ eV to be well within $2\sigma$ of the deviance statistics. We remarkthat measurements at $z=6$ slightly favour a flattening of the LF at faintUV-magnitudes. This tends to prefer some of the non-CDM models in oursimulation suite, although not at a statistically significant level todistinguish them from CDM.

Constraints on dark matter scenarios from measurements of the galaxy luminosity function at high redshifts