The Mira-Titan Universe. III. Emulation of the Halo Mass Function
  We construct an emulator for the halo mass function over group and cluster
mass scales for a range of cosmologies, including the effects of dynamical dark
energy and massive neutrinos. The emulator is based on the recently completed
Mira-Titan Universe suite of cosmological $N$-body simulations. The main set of
simulations spans 111 cosmological models with 2.1 Gpc boxes. We extract halo
catalogs in the redshift range $z=[0.0, 2.0]$ and for masses
$M_{200\mathrm{c}}\geq 10^{13}M_\odot/h$. The emulator covers an 8-dimensional
hypercube spanned by {$\Omega_\mathrm{m}h^2$, $\Omega_\mathrm{b}h^2$,
$\Omega_\nu h^2$, $\sigma_8$, $h$, $n_s$, $w_0$, $w_a$}; spatial flatness is
assumed. We obtain smooth halo mass functions by fitting piecewise second-order
polynomials to the halo catalogs and employ Gaussian process regression to
construct the emulator while keeping track of the statistical noise in the
input halo catalogs and uncertainties in the regression process. For redshifts
$z\lesssim1$, the typical emulator precision is better than $2\%$ for
$10^{13}-10^{14} M_\odot/h$ and $<10\%$ for $M\simeq 10^{15}M_\odot/h$. For
comparison, fitting functions using the traditional universal form for the halo
mass function can be biased at up to 30\% at $M\simeq 10^{14}M_\odot/h$ for
$z=0$. Our emulator is publicly available at
\url{https://github.com/SebastianBocquet/MiraTitanHMFemulator}.
