The e-MANTIS emulator: Fast and accurate predictions of the halo mass function in

Aims. In this work, we present a novel emulator of the halo mass function (HMF), which we implemented in the framework of the <ns0:monospace>e-MANTIS</ns0:monospace> emulator of f(R) gravity models. We also extended <ns0:monospace>e-MANTIS</ns0:monospace> to cover a larger cosmological parameter space and to include models of dark energy with a constant equation of state wCDM. Methods. We used a Latin hypercube sampling of the wCDM 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 Mh ≥ 1013 h−1 M⊙. The typical HMF errors for SO haloes with ∆ = 200c at ɀ = 0 in wCDM (respectively f(R)CDM) are of the order of ϵ0 ≃ 1.5% (ϵ0 ≃ 4%) up to a transition mass Mt ≃ 2 ⋅ 1014 h−1 M⊙ (Mt ≃ 6 ⋅ 1013 h−1 M⊙). For larger masses, the errors are dominated by the shot noise and scale as ϵ0 ⋅ (Mh/Mt)α with α ≃ 0.9 (α ≃ 0.4) up to Mh ~ 1015 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 <ns0:monospace>e-MANTIS</ns0:monospace> is able to better capture the cosmological dependence of the HMF, while being complementary to other existing emulators. Conclusions. The <ns0:monospace>e-MANTIS</ns0:monospace> emulator, which is publicly available, can be used to obtain fast and accurate predictions of the HMF in the f(R)CDM and wCDM 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.