Mixed dark matter: matter power spectrum and halo mass function

We investigate and quantify the impact of mixed (cold warm) dark matter models on large-scale structure observables. In this scenario, comes in two phases, a cold one (CDM) warm (WDM): presence latter causes suppression power spectrum which is allowed by current constraints may be detected present-day upcoming surveys. run large set $N$-body simulations order to build an efficient accurate emulator predict aforementioned with percent precision over wide range values for WDM mass, $M_\mathrm{wdm}$, its fraction respect totality matter, $f_\mathrm{wdm}$. The found independent changes cosmological parameters at 2% level $k\lesssim 10 \ h/$Mpc $z\leq 3.5$. same ranges, applying baryonification procedure both $\Lambda$CDM CWDM account effect feedback, we find similar agreement between scenarios. examine that such has weak lensing angular galaxy clustering spectra. Finally, discuss shape halo mass function analytical prescription yields best simulations. provide reader application cluster number counts.