The ergodicity bias in the observed galaxy distribution

TL;DR

This paper investigates the ergodicity bias in observed galaxy distributions, finding it generally negligible for modern surveys but potentially significant at large scales or low redshifts, impacting cosmological analyses.

Contribution

It provides a numerical analysis of ergodicity bias in galaxy surveys, clarifying its significance and guiding better sample construction and interpretation.

Findings

Ergodicity bias is usually insignificant in modern galaxy surveys.

Bias can become important at large scales or low redshifts.

Careful sample selection is essential for accurate cosmological statistics.

Abstract

The spatial distribution of galaxies we observed is subject to the given condition that we, human beings are sitting right in a galaxy -- the Milky Way. Thus the ergodicity assumption is questionable in interpretation of the observed galaxy distribution. The resultant difference between observed statistics (volume average) and the true cosmic value (ensemble average) is termed as the ergodicity bias. We perform explicit numerical investigation of the effect for a set of galaxy survey depths and near-end distance cuts. It is found that the ergodicity bias in observed two- and three-point correlation functions in most cases is insignificant for modern analysis of samples from galaxy surveys and thus close a loophole in precision cosmology. However, it may become non-negligible in certain circumstances, such as those applications involving three-point correlation function at large scales of local galaxy samples. Thus one is reminded to take extra care in galaxy sample construction and interpretation of the statistics of the sample, especially when the characteristic redshift is low.