A redshift-independent theoretical halo mass function validated with Uchuu simulations

We present a new theoretical framework for the halo mass function (HMF) that accurately predicts the abundance of dark matter halos over an exceptionally wide range of masses and redshifts, based on a generalised Press–Schechter model with triaxial collapse (GPS+). The HMF is formulated mainly as a function of the variance of the linear density field, with a weak explicit mass dependence and no explicit redshift dependence, which is able to naturally reproduce the correct normalisation and high-mass behaviour without requiring an empirical fitting. Using the N-body simulation suite under cosmology, combining six simulations with up to 300 realisations, we measured the HMF over 6.5 łeq łog(M_ Uchuu Planck 200m / h^ M_⊙ -1 ) łeq 16 and 0 łeq z łeq 20 with reduced cosmic variance. Over this full domain, we find that GPS+ matches the simulations to within 10–20%, performing similarly to the Sheth–Tormen model at z łesssim 2, but with substantially results at higher redshifts. In the latter case, the Sheth–Tormen model can deviate by 70–80%, while GPS+ will remain within sim20%. Finally, we show that the halo mass definition is key: M_200m yields a nearly universal, weakly redshift-dependent HMF, whereas adopting the evolving virial overdensity from Bryan $&$ Norman (1998) ends up degrading the agreement at low redshifts and high masses.