Letter to the Editor

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

¹ Instituto de Astrofisica de Andalucia (CSIC) E18008 Granada, Spain
² Instituto de Astrofisica de Canarias C/ Via Lactea s/n Tenerife E38200, Spain
³ Facultad de Fisica, Universidad de La Laguna, Astrofisico Francisco Sanchez s/n La Laguna Tenerife E38200, Spain
⁴ Digital Transformation Enhancement Council, Chiba University, 1-33, Yayoi-cho Inage-ku Chiba 263-8522, Japan
⁵ Department of Astronomy, University of Virginia Charlottesville VA 22904, USA

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 5 December 2025
Accepted: 3 February 2026

Abstract

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 UCHUUN-body simulation suite under Planck cosmology, combining six simulations with up to 300 realisations, we measured the HMF over 6.5 ≤ log(M_200m/[h⁻¹ M_⊙]) ≤ 16 and 0 ≤ z ≤ 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 ≲ 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 ∼20%. 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, G. L. & Norman, M. L. 1998, ApJ, 495, 80) ends up degrading the agreement at low redshifts and high masses.