How much do we know the halo mass function? Predictions beyond resolution

As a common gravitation virialized object in the standard $\Lambda$CDM cosmology, dark matter halo connects from the large-scale structure all the way down to galaxy and star formation. However, as the nature of dark matter particles is still unclear, the smallest halo that can be formed in the universe is still unknown. Based on some simple assumptions, this paper uses the \textsc{hmf} package to investigate different halo functions used to quantify its number and mass distributions -- the halo mass function and the integrated/differential mass function (IMF/DMF) respectively. The halo mass in this study extends from the galaxy cluster to the dark matter particle mass at the GeV scale. Surprisingly, different fitting functions for the HMF are in remarkable agreement, a scatter within 2 orders of magnitude, down to dark matter particle mass, of which the halo mass spans about 80 orders of magnitude and the HMF covers over 100 orders of magnitude. The DMF reveals an interesting and consistent peak at $\sim 10^{13} \hMsun$, which implies galaxy groups have the highest contribution to the total matter mass. Furthermore, the effects of cosmology parameters on these halo functions are also examined with the most massive halos, or these halo functions at the most massive halo mass end, more sensitive to them. Different behaviours of these halo functions due to the changes in cosmology parameters can be used to break the degeneracy between them.