An Analytic Formula for the Supercluster Mass Function
  We present an analytic formula for the supercluster mass function which is
constructed by modifying the extended Zel'dovich model for the halo mass
function. The formula has two characteristic parameters whose best-fit values
are determined by fitting to the numerical results from N-body simulations for
the standard LambdaCDM cosmology. The parameters are found to be independent of
redshifts and robust against variation of the key cosmological parameters.
Under the assumption that the same formula for the supercluster mass function
is valid for non-standard cosmological models, we show that the relative
abundance of the rich superclusters should be a powerful indicator of any
deviation of the real universe from the prediction of the standard LambdaCDM
model.
