The scale of cosmic homogeneity as a standard ruler

In this paper, we study the characteristic scale of transition to cosmic homogeneity of the universe, $\mathcal{R}_H$, as a standard ruler, to constrain cosmological parameters on mock galaxy catalogues. We use mock galaxy catalogues that simulate the CMASS galaxy sample of the BOSS survey in the redshift range $0.43 \leq z \leq 0.7$. In each redshift bin we obtain the homogeneity scale, defined as the scale at which the universe becomes homogeneous to $1\%$, i.e. $D_2(\mathcal{R}_H) = 2.97$. With a simple Fisher analysis, we find that the performance of measuring the cosmological parameters with either the position of the BAO peak or the homogeneity scale is comparable. We show that $\mathcal{R}_H$ has a dependence on the galaxy bias. If the accuracy and precision of this bias is achieved to $1\%$, as expected for future surveys, then $\mathcal{R}_H$ is a competitive standard ruler.