The Sheth–Tormen approximation is a halo mass function.
The Sheth–Tormen approximation extends the Press–Schechter formalism by assuming that halos are not necessarily spherical, but merely elliptical. The distribution of the density fluctuation is as follows: , where , , and . [1] The parameters were empirically obtained from the five-year release of WMAP. [2]
In 2010, the Bolshoi Cosmological Simulation predicted that the Sheth–Tormen approximation is inaccurate for the most distant objects. Specifically, the Sheth–Tormen approximation overpredicts the abundance of haloes by a factor of for objects with a redshift , but is accurate at low redshifts. [3] [2]