Constraining the halo mass function with observations
  The abundances of dark matter halos in the universe are described by the halo
mass function (HMF). It enters most cosmological analyses and parametrizes how
the linear growth of primordial perturbations is connected to these abundances.
Interestingly, this connection can be made approximately cosmology independent.
This made it possible to map in detail its near-universal behavior through
large-scale simulations. However, such simulations may suffer from systematic
effects, especially if baryonic physics is included. In this paper we ask how
well observations can constrain directly the HMF. The observables we consider
are galaxy cluster number counts, galaxy cluster power spectrum and lensing of
type Ia supernovae. Our results show that DES is capable of putting the first
meaningful constraints on the HMF, while both Euclid and J-PAS can give
stronger constraints, comparable to the ones from state-of-the-art simulations.
We also find that an independent measurement of cluster masses is even more
important for measuring the HMF than for constraining the cosmological
parameters, and can vastly improve the determination of the halo mass function.
Measuring the HMF could thus be used to cross-check simulations and their
implementation of baryon physics. It could even, if deviations cannot be
accounted for, hint at new physics.
