# Exploring cosmic homogeneity with the BOSS DR12 galaxy sample

## TL;DR

This paper uses the largest galaxy survey to measure the scale at which the universe becomes homogeneous, confirming the predictions of the Lambda Cold Dark Matter model and supporting the Cosmological Principle.

## Contribution

It provides a precise measurement of the cosmic homogeneity scale using the BOSS DR12 galaxy sample, extending previous results and testing the Lambda CDM model's predictions.

## Key findings

- Homogeneity scale found at 63.3 Mpc/h, consistent with Lambda CDM predictions.
- Homogeneity scale shows no significant redshift evolution, aligning with theoretical expectations.
- Fractal correlation dimension approaches 3 at scales larger than 300 Mpc/h.

## Abstract

In this study, we probe the transition to cosmic homogeneity in the Large Scale Structure (LSS) of the Universe using the CMASS galaxy sample of BOSS spectroscopic survey which covers the largest effective volume to date, $3\ h^{-3}\ \mathrm{Gpc}^3$ at $0.43 \leq z \leq 0.7$. We study the scaled counts-in-spheres, $\mathcal{N}(<r)$, and the fractal correlation dimension, $\mathcal{D}_2(r)$, to assess the homogeneity scale of the universe using a $Landy\ \&\ Szalay$ inspired estimator. Defining the scale of transition to homogeneity as the scale at which $\mathcal{D}_2(r)$ reaches 3 within $1\%$, i.e. $\mathcal{D}_2(r)>2.97$ for $r>\mathcal{R}_H$, we find $\mathcal{R}_H = (63.3\pm0.7) \ h^{-1}\ \mathrm{Mpc}$, in agreement at the percentage level with the predictions of the $\Lambda$CDM model $\mathcal{R}_H=62.0\ h^{-1}\ \mathrm{Mpc}$. Thanks to the large cosmic depth of the survey, we investigate the redshift evolution of the transition to homogeneity scale and find agreement with the $\Lambda$CDM prediction. Finally, we find that $\mathcal{D}_2$ is compatible with $3$ at scales larger than $300\ h^{-1}\ $Mpc in all redshift bins. These results consolidate the Cosmological Principle and represent a precise consistency test of the $\Lambda CDM$ model.