The cosmological mass function in the Zel'dovich approximation.

The Press-Schechter theory of the cosmological mass function and its modifications allow constraint of cosmological scenarios of structure formation. Recently, a few new models that explored the influence of anisotropic collapse on the shape of the mass function have been suggested. I discuss in more detail a particular model that assumes a fluid particle becomes part of a gravitationally bound halo when the smallest eigenvalue of the deformation tensor of the filtered initial density field reaches a certain threshold (like the filtered density contrast reaches the threshold in the Press-Schechter formalism). Choosing the smallest eigenvalue guarantees that the fluid particle in question experiences collapse along all three axes. The model shows a better agreement with the N-body simulations than with the standard Press-Schechter model.