# A high precision semi-analytic mass function

## TL;DR

This paper presents a high-precision semi-analytic mass function for cosmic structures, incorporating cosmological constant, angular momentum, and dynamical friction, matching simulations within 3% accuracy across a wide mass and redshift range.

## Contribution

It introduces an improved barrier in the excursion set approach that accounts for key physical effects, enhancing the accuracy of mass function predictions.

## Key findings

- Agreement within 3% with Bolshoi simulation for a wide mass and redshift range.
- Consistent results with Bhattacharya's fitting formula for galaxy cluster masses.
- Demonstrates the model's applicability across different cosmologies.

## Abstract

In this paper, extending past works of Del Popolo, we show how a high precision mass function (MF) can be obtained using the excursion set approach and an improved barrier taking implicitly into account a non-zero cosmological constant, the angular momentum acquired by tidal interaction of proto-structures and dynamical friction. In the case of the $\Lambda$CDM paradigm, we find that our MF is in agreement at the 3\% level to Klypin's Bolshoi simulation, in the mass range $M_{\rm vir} = 5 \times 10^9 h^{-1} M_{\odot} -- 5 \times 10^{14} h^{-1} M_{\odot}$ and redshift range $0 \lesssim z \lesssim 10$. For $z=0$ we also compared our MF to several fitting formulae, and found in particular agreement with Bhattacharya's within 3\% in the mass range $10^{12}-10^{16} h^{-1} M_{\odot}$. Moreover, we discuss our MF validity for different cosmologies.