  Existing models for the dependence of the halo mass function on cosmological
parameters will become a limiting source of systematic uncertainty for cluster
cosmology in the near future. We present a halo mass function emulator and
demonstrate improved accuracy relative to state-of-the-art analytic models. In
this work, mass is defined using an overdensity criteria of 200 relative to the
mean background density. Our emulator is constructed from the AEMULUS
simulations, a suite of 40 N-body simulations with snapshots from z=3 to z=0.
These simulations cover the flat wCDM parameter space allowed by recent Cosmic
Microwave Background, Baryon Acoustic Oscillation and Type Ia Supernovae
results, varying the parameters w, Omega_m, Omega_b, sigma_8, N_{eff}, n_s, and
H_0. We validate our emulator using five realizations of seven different
cosmologies, for a total of 35 test simulations. These test simulations were
not used in constructing the emulator, and were run with fully independent
initial conditions. We use our test simulations to characterize the modeling
uncertainty of the emulator, and introduce a novel way of marginalizing over
the associated systematic uncertainty. We confirm non-universality in our halo
mass function emulator as a function of both cosmological parameters and
redshift. Our emulator achieves better than 1% precision over much of the
relevant parameter space, and we demonstrate that the systematic uncertainty in
our emulator will remain a negligible source of error for cluster abundance
studies through at least the LSST Year 1 data set.
