Investigating cosmic homogeneity using multifractal analysis of the SDSS-IV eBOSS DR16 quasar catalogue

Abstract

ABSTRACT We analyse the volume-limited subsamples extracted from the sixteenth data release of the Sloan Digital Sky Survey-IV (SDSS-IV) eBOSS quasar survey spanning a redshift interval of 0.8 < z < 2.2, to estimate the scale of transition to homogeneity in the Universe. The multifractal analysis used for this purpose considers the scaling behaviour of different moments of quasar distribution in different density environments. This analysis gives the spectrum of generalized dimension Dq, where positive values of q characterize the scaling behaviour in overdense regions and the negative ones in underdense regions. We expect fractal correlation dimension Dq(r) = 3, for a homogeneous, random point distribution in 3-Dimensions. The fractal correlation dimension Dq(r), corresponding to q = 2 obtained in our study stabilizes in the range (2.8–2.9) for scales r > 80 h−1 Mpc. The observed quasar distribution shows consistency with the simulated mock data and the random distribution of quasars within one sigma. Further, the generalized dimension spectrum Dq(r) also reveals transition to homogeneity beyond >110 h−1 Mpc, and the dominance of clustering at small scales r < 80 h−1 Mpc. Consequently, our study provides strong evidence for the homogeneity in SDSS quasar distribution, offering insights into large-scale structure properties and, thus can play a pivotal role in scrutinizing the clustering properties of quasars and its evolution in various upcoming surveys such as Dark Energy Spectroscopic Instrument and Extremely Large Telescope.