The e-MANTIS emulator: fast and accurate predictions of the halo mass function in $f(R)$CDM and $w$CDM cosmologies

In this work, we present a novel emulator of the halo mass function, which we implement in the framework of the e-mantis emulator of $f(R)$ gravity models. We also extend e-mantis to cover a larger cosmological parameter space and to include models of dark energy with a constant equation of state $w$CDM. We use a Latin hypercube sampling of the $w$CDM and $f(R)$CDM cosmological parameter spaces, over a wide range, and realize a large suite of more than $10000$ $N$-body simulations of different volume, mass resolution and random phase of the initial conditions. For each simulation in the suite, we generate halo catalogues using the friends-of-friends halo finder, as well as the spherical overdensity algorithm for different overdensity thresholds. We decompose the corresponding halo mass functions on a B-spline basis, and use this decomposition to train an emulator based on Gaussian processes. The resulting emulator is able to predict the halo mass function for redshifts $\le 1.5$ and for halo masses $M_h\ge {10}^{13}{h}^{-1}{M}_{\odot }$. The typical HMF errors for SO haloes with $\mathrm{\Delta }=200\mathrm{c}$ at $z=0$ in $w$CDM (respectively $f(R)$CDM) are of order of ${\epsilon }_0\simeq 1.5\mathrm{\%}$ (${\epsilon }_0\simeq 4\mathrm{\%}$) up to a transition mass $M_t\simeq 2\cdot {10}^{14}{h}^{-1}{M}_{\odot }$ ($M_t\simeq 6\cdot {10}^{13}{h}^{-1}{M}_{\odot }$). For larger masses, the errors are dominated by shot-noise and scale as ${\epsilon }_0\cdot {\left(M_h\mathrm{/}{M}_t\right)}^{\alpha }$ with $\alpha \simeq 0.9$ ($\alpha \simeq 0.4$) up to $M_h\sim {10}^{15}{h}^{-1}{M}_{\odot }$. Independently of this general trend, the emulator is able to provide an estimation of its own error as a function of the cosmological parameters, halo mass, and redshift. The e-mantis emulator, which is publicly available, can be used to obtain fast and accurate predictions of the halo mass function in the $f(R)$CDM and $w$CDM non-standard cosmological models.