The e-MANTIS emulator: Fast and accurate predictions of the halo mass function in <i>f</i>(<i>R</i>)CDM and <i>w</i>CDM cosmologies

Aims . 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. Methods . 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 10 000 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. Results . The resulting emulator is able to predict the HMF for redshifts ≤1.5 and for halo masses M h ≥ 10 13 h −1 M ⊙ . The typical HMF errors for SO haloes with ∆ = 200c at ɀ = 0 in w CDM (respectively f ( R )CDM) are of the order of ϵ 0 ≃ 1.5% ( ϵ 0 ≃ 4%) up to a transition mass M t ≃ 2 ⋅ 10 14 h −1 M ⊙ ( M t ≃ 6 ⋅ 10 13 h −1 M ⊙ ). For larger masses, the errors are dominated by the shot noise and scale as ϵ 0 ⋅ ( M h / M t ) α with α ≃ 0.9 ( α ≃ 0.4) up to M h ~ 10 15 h −1 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. Conclusions . 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.