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