# Can the homogeneity scale be used as a standard ruler?

## TL;DR

This paper critically evaluates whether the homogeneity scale can serve as a reliable standard ruler in cosmology, concluding it is unsuitable due to its non-monotonic behavior with matter density and minimal impact from redshift space distortions.

## Contribution

The study provides a theoretical and simulation-based analysis showing the homogeneity scale cannot be used as a standard ruler in the b1CDM model due to its non-monotonic dependence on matter density.

## Key findings

- Homogeneity scale is non-monotonic with b5_m0 in b1CDM.
- Redshift space distortions do not significantly alter the homogeneity scale.
- N-Body simulations confirm the theoretical results.

## Abstract

The Universe on comoving scales larger than 100 Mpc/h is assumed to be statistically homogeneous, with the transition scale where we have $1\%$ deviation from homogeneity being known as the homogeneity scale $R_H$. The latter was recently proposed in Ntelis et al. (2018) [arXiv:1810.09362] to be a standard ruler. In this paper we perform a comparison between the baryon acoustic oscillations and the homogeneity scales $R_H$, assuming a spatially flat universe, linear cosmological perturbation theory and the cosmological constant cold dark matter $\Lambda$CDM model. By direct theoretical calculations, we demonstrate that the answer to the question of whether the homogeneity scale can be used as a standard ruler, is clearly negative due to the non-monotonicity of the homogeneity scale $R_H$ with the matter density parameter $\Omega_{m0}$ of the $\Lambda$CDM model. Furthermore, we also consider the effect of redshift space distortions and we find that they do not break the degeneracies but instead only change the value of $R_H$ by a few percent. Finally, we also confirm our findings with the help of an N-Body simulation.