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

In this work, we present a novel emulator of the halo mass function (HMF), which we implemented in the framework of the e-MANTIS emulator of $f(R)$ gravity models. We also extended 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 used a Latin hypercube sampling of the $w$CDM and $f(R)$CDM cosmological parameter spaces, over a wide range, and carried out a large suite of more than $10000$ $N$-body simulations with a different volume, mass resolution, and random phase for the initial conditions. For each simulation in the suite, we generated halo catalogues using the friends-of-friends (FoF) halo finder, as well as the spherical overdensity (SO) algorithm for different overdensity thresholds (200, 500, and 1000 times the critical density). We decomposed the corresponding HMFs on a B-spline basis, while adopting a minimal set of assumptions on their shape. We used this decomposition to train an emulator based on Gaussian processes. The resulting emulator is able to predict the HMF for redshifts $ 1.5$ and for halo masses $M_h M_ The typical HMF errors for SO haloes with $ c $ at $z=0$ in $w$CDM (respectively $f(R)$CDM) are of the order of $ up to a transition mass $M_t M_ ($M_t M_ For larger masses, the errors are dominated by the shot noise and scale as $ with $ up to $M_h M_ 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. We have performed an extensive comparison against analytical parametrizations and shown that e-MANTIS is able to better capture the cosmological dependence of the HMF, while being complementary to other existing emulators. The e-MANTIS emulator, which is publicly available, can be used to obtain fast and accurate predictions of the HMF in the $f(R)$CDM and $w$CDM non-standard cosmological models. As such, it represents a useful theoretical tool to constrain the nature of dark energy using data from galaxy cluster surveys.