Investigation of homogeneity and matter distribution on large scales using large quasar groups

TL;DR

This study analyzes large quasar groups across different redshifts to assess the universe's homogeneity, finding that LQGs are more biased at higher redshifts and that the homogeneity scale supports the cosmological principle.

Contribution

It provides new measurements of the homogeneity scale of LQGs using three dark matter halo profiles, challenging standard structure growth predictions.

Findings

Higher redshift LQGs are more biased and correlated.

Homogeneity scales range from 224 to 390 h^{-1} Mpc across redshift bins.

Results support the cosmological principle at large scales.

Abstract

We use 12 large quasar group (LQG) samples to investigate the homogeneity of $0.5\lesssim z \lesssim 2$ Universe ($z$ denotes the redshift). We calculate the bias factor $b$ and the two-point correlation function $\xi_{{\rm LQG}}$ for such groups for three different density profiles of the LQG dark matter halos, i.e. the isothermal profile, the Navarro-Frenk-White (NFW) profile, and the (gravitational) lensing profile. We consider the $\Lambda$CDM concordance model of our Universe with $\Omega_m=0.28$, $\Omega_\Lambda=0.72$, the Hubble constant $H_0=100h~$km s$^{-1}$ Mpc$^{-1}$ with $h=0.72$ in our calculations. Dividing the samples into three redshift bins, we find that the LQGs with higher redshift are more biased and correlated than those with lower redshift. The redshift-increasing LQG correlation amplitudes we find is incompatible with that predicted by the standard theory of structure growth. The homogeneity scale $R_H$ of the LQG distribution is also deduced. It is defined as the comoving radius of the sphere inside which the number of LQGs $N(<r)$ is proportional to $r^3$ within $1\%$, or equivalently above which the correlation dimension of the sample $D_2$ is within $1\%$ of $D_2=3$. For the NFW dark matter halo profile, the homogeneity scales of the LQG distribution are $R_H\simeq 224$ $h^{-1}$Mpc for $0.5< z\leq 1$, $R_H\simeq 316$ $h^{-1}$Mpc for $1< z\leq 1.5$, and $R_H\simeq 390$ $h^{-1}$Mpc for $1.5< z\lesssim 2$. These values are above the characteristic sizes of the LQG samples in each bin, implying the validity of the cosmological principle on the LQG scale, i.e. a length range of $200\sim 400~h^{-1}$Mpc and a mass scale of $\sim 10^{14}$M$_\odot$. ...