An Analytic Formula for the Supercluster Mass Function

TL;DR

This paper introduces an analytic formula for the supercluster mass function based on a modified Zel'dovich model, fitting well with simulations and potentially serving as a tool to test cosmological models.

Contribution

It provides a new analytic formula for the supercluster mass function with parameters that are robust across cosmologies and redshifts.

Findings

Parameters are independent of redshift.

Parameters are robust against cosmological variations.

The formula can test deviations from LambdaCDM.

Abstract

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.