Measuring the cosmic homogeneity scale with SDSS-IV DR16 Quasars

TL;DR

This paper measures the cosmic homogeneity scale using SDSS-IV DR16 quasars, confirming the standard cosmological model's prediction of a transition to homogeneity at large scales across redshifts 2.2 to 3.2.

Contribution

First measurement of the cosmic homogeneity scale using quasar data from SDSS-IV DR16 across multiple redshifts.

Findings

Homogeneity scale decreases with increasing redshift.

Results agree with $\ m\Lambda$CDM predictions.

Supports the standard cosmological model's assumptions.

Abstract

We report measurements of the scale of cosmic homogeneity ($r_{h}$) using the recently released quasar sample of the sixteenth data release of the Sloan Digital Sky Survey (SDSS-IV DR16). We perform our analysis in 2 redshift bins lying in the redshift interval $2.2 < z < 3.2$ by means of the fractal dimension $D_2$. By adopting the usual assumption that $r_{h}$ is obtained when $D_2 \sim 2.97$, that is, within 1% of $D_2=3$, we find the cosmic homogeneity scale with a decreasing trend with redshift, and in good agreement with the $\Lambda$CDM prediction. Our results confirm the presence of a homogeneity scale in the spatial distribution of quasars as predicted by the fundamental assumptions of the standard cosmological model.