The halo mass function in alternative dark matter models
  The claimed detection of large amounts of substructure in lensing flux
anomalies, and in Milky Way stellar stream gaps statistics, has lead to a step
change in constraints on simple warm dark matter models. In this study we
compute predictions for the halo mass function both for these simple models and
also for comprehensive particle physics models of sterile neutrinos and dark
acoustic oscillations. We show that the mass function fit of Lovell et al.
underestimates the number of haloes less massive than the half-mode mass,
$M_\mathrm{hm}$ by a factor of 2, relative to the extended Press-Schechter
(EPS) method. The alternative approach of applying EPS to the Viel et al.
matter power spectrum fit instead suggests good agreement at $M_\mathrm{hm}$
relative to the comprehensive model matter power spectra results, although the
number of haloes with mass $<M_\mathrm{hm}$ is still suppressed due to the
absence of small scale power in the fitting function. Overall, we find that the
number of dark matter haloes with masses $<10^{8}M_{\odot}$ predicted by
competitive particle physics models is underestimated by a factor of $\sim2$
when applying popular fitting functions, although careful studies that follow
the stripping and destruction of subhaloes will be required in order to draw
robust conclusions.
