Effects of Smoothing Functions in Cosmological Counts-in-Cells Analysis

Abstract

Abstract A method for a counts-in-cells analysis of the galaxy distribution is investigated with arbitrary smoothing functions for obtaining the galaxy counts. We explore the possiblity of optimizing the smoothing function, while considering a series of $m$-weight Epanechnikov kernels. The popular top-hat and Gaussian smoothing functions are two special cases in this series. In this paper, we mainly consider the second moments of counts-in-cells as a first step. We have analytically derived the covariance matrix among different smoothing scales of cells, while taking into account possible overlaps between cells. We find that the Epanechnikov kernel of $m=1$ is better than top-hat and Gaussian smoothing functions in estimating cosmological parameters. As an example, we estimated expected parameter bounds that come only from an analysis of the second moments of the galaxy distributions in a survey that is similar to the Sloan Digital Sky Survey.