The Homogeneity Scale of the universe

TL;DR

This paper investigates the scale at which the universe appears homogeneous using galaxy data, confirming the Cosmological Principle and examining how this scale evolves with redshift.

Contribution

It provides the first precise measurement of the universe's homogeneity scale using BOSS CMASS data and tests its evolution across redshift.

Findings

Homogeneity scale is approximately 64.3 h^{-1} Mpc.

Universe is homogeneous on scales larger than this scale.

Results support the Cosmological Principle within the DM model.

Abstract

In this study, we probe the cosmic homogeneity with the BOSS CMASS galaxy sample in the redshift region of $0.43 < z < 0.7$. We use the normalised counts-in-spheres estimator $\mathcal{N}(<r)$ and the fractal correlation dimension $\mathcal{D}_{2}(r)$ to assess the homogeneity scale of the universe. We verify that the universe becomes homogenous on scales greater than $\mathcal{R}_{H} \simeq 64.3\pm1.6\ h^{-1}Mpc$, consolidating the Cosmological Principle with a consistency test of $\Lambda$CDM model at the percentage level. Finally, we explore the evolution of the homogeneity scale in redshift.