The scale of cosmic homogeneity as a standard ruler

TL;DR

This study investigates the use of the universe's transition to cosmic homogeneity scale as a standard ruler to constrain cosmological parameters, demonstrating its potential competitiveness with BAO measurements in future surveys.

Contribution

The paper introduces the homogeneity scale as a new standard ruler for cosmology and analyzes its effectiveness compared to traditional methods using mock galaxy data.

Findings

Homogeneity scale can serve as a standard ruler with comparable performance to BAO.

The homogeneity scale depends on galaxy bias, affecting its use.

Future surveys can achieve the necessary bias precision for this method to be effective.

Abstract

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.