Mass function of haloes: scale invariant models
  Press-Schechter theory gives a simple, approximate functional form of the
mass function of dark matter haloes. Sheth and Tormen (ST) refined this mass
function to give an improved analytical fit to results of N-body simulations.
These forms of the halo mass function are universal (independent of cosmology
and power spectrum) when scaled in suitable variables. Using large suites of
LCDM N-body simulations, studies in the last few years have shown that this
universality is only approximate. We explore whether some of the deviations
from universality can be attributed to the power spectrum by computing the mass
function in N-body simulations of various scale-free models in an Einstein-de
Sitter cosmology. This choice of cosmology does not introduce any scale into
the problem. These models have the advantage of being self-similar, hence
stringent checks can be imposed while running these simulations. This set of
numerical experiments is designed to isolate any power spectrum dependent
departures from universality of mass functions. We show explicitly that the
best fit ST parameters have a clear dependence on power spectrum. Our results
also indicate that an improved analytical theory with more parameters is
required in order to provide better fits to the mass function.
