Testing Cosmic Homogeneity Using Galaxy Clusters

TL;DR

This study tests the cosmological principle by analyzing galaxy cluster sizes and densities across large volumes, finding consistent averages supporting homogeneity, and comparing observations with simulations to understand cluster evolution.

Contribution

It provides empirical evidence for cosmic homogeneity using SDSS data and compares results with simulations, highlighting discrepancies in cluster amplitude evolution.

Findings

Cluster sizes and densities are consistent across 2 Gpc/h regions.

Average cluster size remains constant within 10% up to redshift 0.25.

Observed increase in cluster amplitudes with redshift is due to sample composition, not cosmological effects.

Abstract

According to the cosmological principle, galaxy cluster sizes and cluster densities, when averaged over sufficiently large volumes of space, are expected to be constant everywhere, except for a slow variation with look-back time (redshift). Thus, average cluster sizes or correlation lengths provide a means of testing for homogeneity that is almost free of selection biases. Using ~10^6 galaxies from the SDSS DR7 survey, I show that regions of space separated by ~2 Gpc/h have the same average cluster size and density to 5 - 10 percent. I show that the average cluster size, averaged over many galaxies, remains constant to less than 10 percent from small redshifts out to redshifts of 0.25. The evolution of the cluster sizes with increasing redshift gives fair agreement when the same analysis is applied to the Millennium Simulation. However, the MS does not replicate the increase in cluster amplitudes with redshift seen in the SDSS data. This increase is shown to be caused by the changing composition of the SDSS sample with increasing redshifts. There is no evidence to support a model that attributes the SN Ia dimming to our happening to live in a large, nearly spherical void.