Joint halo mass function for modified gravity and massive neutrinos I:
  simulations and cosmological forecasts
  We present a halo mass function accurate over the full relevant Hu-Sawicki
$f(R)$ parameter space based on spherical collapse calculations and calibrated
to a suite of modified gravity $N$-body simulations that include massive
neutrinos. We investigate the ability of current and forthcoming galaxy cluster
observations to detect deviations from general relativity while constraining
the total neutrino mass and including systematic uncertainties. Our results
indicate that the degeneracy between massive neutrino and modify gravity
effects is a limiting factor for the current searches for new gravitational
physics with clusters of galaxies, but future surveys will be able to break the
degeneracy.
