Investigating Cosmic Homogeneity Using Multi-fractal Analysis of the SDSS-IV eBOSS DR16 Quasar Catalog

Abstract

We analyze the volume-limited subsamples extracted from the sixteenth data release of the 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 multi-fractal analysis used for this purpose considers the scaling behavior 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 behavior in over-dense regions and the negative ones in under-dense 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 scales𝑟 < 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 (DESI) and Extremely Large Telescope (ELT).