Using SDSS DR16 LRG Sample To Investigate The Homogeneity Of Large-scale Structure Of The Universe

One of the theoretical foundations of modern cosmology is the so-called cosmological principle which states that the universe is homogeneous and isotropic in the large-scale.With the advent of the era of precise cosmology,it is possible to test cosmological principles from observations.So far,the analysis of the survey data has been able to show the isotropic nature of the large-scale structure,but it is still controversial whether the distribution of galaxies on large-scale structure is homogeneous.This is reflected in the fact that there is not yet a generally accepted homogeneity-scale of large-scale structure.According to the standard cosmological method,the analysis of the survey data shows that the distribution of galaxies in the observable universe is imhomogeneous in small scales(<100Mpc/h)with a fractal distribution.On the larger scale,it is well believed that there is a homogeneity-scale rh,beyond it the distribution of galaxies is homogeneous.At present,many studies try to determine the homogeneity-scale rh from the survey data,so as to determine the validity of cosmological principle.In this paper,we obtain and process the latest data release DR16 of Sloan Digital Sky Survey(SDSS).Using the eBOSS luminous red Galaxy(LRG)data sample,we calculate the two-point correlation function ?(r)of the sample data,and preliminarily obtain the range of homogeneity-scale rh,which is 156-216 Mpc/h.Meanwhile,we determine the character scale r0,which is between 5-16 Mpc/h.Our results are basically consistent with the theoretical prediction of the standard cosmological model(?CDM model).However,on the other hand,we must point out that if we regard the large-scale structure of the universe as a complex system,there is a certain "tension" between standard cosmology and statistical physics in the definition of homogeneity-scale.This may leads to significant differences in the understanding(and calculations)of homogeneity-scale.The current present preliminary calculations in this paper lay a foundation for further investigation of large-scale structures in the near future.