Aemulus $\nu$: Precision halo mass functions in w$\nu$CDM cosmologies

Precise and accurate predictions of the halo mass function for cluster mass scales in $w\nu{\rm CDM}$ cosmologies are crucial for extracting robust and unbiased cosmological information from upcoming galaxy cluster surveys. Here, we present a halo mass function emulator for cluster mass scales ($\gtrsim 10^{13}M_\odot /h$) up to redshift $z=2$ with comprehensive support for the parameter space of $w\nu{\rm CDM}$ cosmologies allowed by current data. Based on the Aemulus $\nu$ suite of simulations, the emulator marks a significant improvement in the precision of halo mass function predictions by incorporating both massive neutrinos and non-standard dark energy equation of state models. This allows for accurate modeling of the cosmology dependence in large-scale structure and galaxy cluster studies. We show that the emulator, designed using Gaussian Process Regression, has negligible theoretical uncertainties compared to dominant sources of error in future cluster abundance studies. Our emulator is publicly available, providing the community with a crucial tool for upcoming cosmological surveys such as LSST and Euclid.