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.