The angular scale of homogeneity with SDSS-IV DR16 Luminous Red Galaxies

TL;DR

This study measures the angular scale of cosmic homogeneity using SDSS-IV LRG data with a model-independent approach, confirming consistency with standard cosmology predictions across specific redshift ranges.

Contribution

It introduces a model-independent method to measure the angular scale of homogeneity using only celestial coordinates of LRGs, avoiding projection biases.

Findings

Measured angular homogeneity scale consistent with standard cosmology

Results agree with mock catalogues based on the standard model

Provides bootstrap uncertainties for the homogeneity scale

Abstract

We report measurements of the angular scale of cosmic homogeneity ($\theta_{H}$) using the recently released luminous red galaxy sample of the sixteenth data release of the Sloan Digital Sky Survey (SDSS-IV LRG DR16). It consists of a model-independent method, as we only use the celestial coordinates of these objects to carry out such an analysis. The observational data is divided into thin redshift bins, namely $0.67<z<0.68$, $0.70<z<0.71$, and $0.73<z<0.74$, in order to avoid projection biases, and we estimate our uncertainties through a bootstrap method and a suite of mock catalogues. We find that the LRGs exhibit an angular scale of homogeneity consistent with the predictions of the standard cosmology within the redshift interval studied. Considering the bootstrap method, in which the measurements are obtained in a model-independent way, we found at 1$\sigma$ level that $\theta_H^{boot}(0.675) = 7.57 \pm 2.91$ deg, $\theta_H^{boot} (0.705) = 7.49 \pm 2.63$ deg and $\theta_H^{boot} (0.735) = 8.88 \pm 2.81$ deg. Such results are in good agreement with the ones obtained using mock catalogues built under the assumption of the standard cosmological model.