Can the homogeneity scale be used as a standard ruler?

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.

6 pages, 4 figures. Comments welcome. Changes match published version

References in corpus (3)

• Homogeneity and isotropy in the 2MASS Photometric Redshift catalogue
• Absence of self-averaging and of homogeneity in the large scale galaxy distribution
• Evidence for an environment-dependent shift in the baryon acoustic oscillation peak

Cited by in corpus (1)

• The angular scale of homogeneity in the Local Universe with the SDSS blue galaxies