Cosmological constraints from cosmic homogeneity

Abstract

In this paper, we study the normalised characteristic scale of transition to cosmic homogeneity, ${\mathcal{R}}_H/d_V$, as a cosmological probe. We use a compilation of SDSS galaxy samples, comprising more than $10^6$ galaxies in the redshift range $0.17\le z\le 2.2$ within the largest comoving volume to date, $\sim 8h^{-3}{\mathrm{Gpc}}^3$. We show that these samples can be described by a single bias model as a function of redshift. By combining our measurements with prior Cosmic Microwave Background and Lensing information from the Planck satellite, we constrain the total matter density ratio of the universe, $\hat{I}{\text{c◯}}_m=0.363\pm 0.025$, and the Dark Energy density ratio, $\hat{I}{\text{c◯}}_{\hat{I}}›=0.649\pm 0.021$, improving the values from Planck alone by 31% and 28%, respectively. Our results are compatible with a flat $\hat{I}›$CDM model. These results show the complementarity of the normalised homogeneity scale with other cosmological probes and open new roads to cosmometry.

27 pages, 7 figures, prepared for submission to JCAP