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.
Categories: astro-ph.CO