Cosmological constraints from cosmic homogeneity

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 the SDSS galaxy samples, comprising more than $10^6$ galaxies in the redshift range $0.17 leq z leq 2.2$ within the largest comoving volume to date, $sim 8 h^{-3}Gpc^3$. 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 $Omega_m = 0.340 pm 0.029$ and the Dark Energy density ratio $Omega_{Lambda} = 0.668 pm 0.023$. Our results are compatible with a flat $Lambda$CDM model. These results show the complementarity of the normalised homogeneity scale with other cosmological probes and open new roads to cosmometry.