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, 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 ≤ z ≤ 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. D2(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 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 H is a competitive standard ruler.