A high precision semi-analytic mass function

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 $\mathrm{\Lambda }$CDM paradigm, we find that our MF is in agreement at the 3% level to Klypin’s Bolshoi simulation, in the mass range $M_{\rm vir} = 5 \times 10^9 h^{-1} M_{\odot} – 5 \times 10^{14} h^{-1} M_{\odot}$andredshiftrange$0 \lesssim z \lesssim 10$\mathrm{.}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.