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 RH. The latter was recently proposed in Ntelis et al. [J. Cosmol. Astropart. Phys. 12 (2018) 014JCAPBP1475-751610.1088/1475-7516/2018/12/014] to be a standard ruler. In this paper we perform a comparison between the baryon acoustic oscillations and the homogeneity scales RH, assuming a spatially universe, linear cosmological perturbation theory and the cosmological constant cold dark matter (ΛCDM) 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 nonmonotonicity of the homogeneity scale RH with the matter density parameter Ωm0 of the ΛCDM 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 RH by a few percent. Finally, we also confirm our findings with the help of an N-body simulation.