Homogeneity scale in the local Universe: Model-independent estimate from S-PLUS iDR6 blue galaxies

Abstract

We present a model-independent estimate of the angular homogeneity scale in the local Universe by analysing data from the Southern Photometric Local Universe Survey (S-PLUS). Two complementary estimators are employed: (i) a parametric approach fitting the power-law of the two-point angular correlation function, which yields the homogeneity scale ${\theta }_H=8.94_{-3.38}^{+1.20}\mathrm{deg}$; and (ii) a nonparametric fractal correlation dimension method, computing ${\mathcal{D}}_2(\theta )$ directly from the correlation function, which results in ${\theta }_H=7.91_{-2.94}^{+5.50}\mathrm{deg}$. We apply both methodologies to a set of mock catalogs, generated with the Generator for Large Scale Structure algorithm, and find that both estimates are well within $1\sigma$ of their respective median values. The transition scale to homogeneity, according to the $\Lambda$ cold dark matter (CDM) model, is defined for matter, i.e., $b=1$. Measurements of this scale with observational data clearly depend on the cosmic tracer analyzed, and a calibration is necessary. Our study with blue galaxies, with bias $b\simeq 1$, provides a suitable estimate for comparison. Indeed, the results obtained in both approaches are compared with the value expected in the $\Lambda$CDM model, obtaining a good concordance.

12 pages, 9 figures, 3 appendix