Probing Large-scale Structures with the Two-point Function and the Power Spectrum: Insights into Cosmic Clustering Evolution

Abstract Understanding the large-scale structure of the Universe requires analyses of cosmic clustering and its evolution over time. In this work, we investigate the clustering properties of Sloan Digital Sky Survey blue galaxies, which are excellent tracers of dark matter, along two distinct epochs of the Universe, utilizing estimators like the two-point angular correlation function (2PACF), the angular power spectra, among others. Considering a model-independent approach, we perform analyses in two disjoint redshift shells, 0 ≤ z < 0.06 and 0.06 ≤ z < 0.12, to investigate the distribution of large cosmic structures. Using Bayesian inference methods, we constrain the parameter that quantifies the galaxy clustering in the 2PACF, enabling us to perform comparisons among different regions on the sky and between different epochs in the Universe regarding the gravitational action on matter structures. Our analyses complement previous efforts to map large-scale structures in the Local Universe. In addition, this study reveals differences regarding the clustering of large cosmic structures, comparing two epochs of the Universe, and analyses done with diverse estimators. Results reveal, clearly, distinct evolutionary signatures between the two redshift shells. Moreover, we had the opportunity to test the concordance cosmological model under extreme conditions in the highly nonlinear Local Universe, computing the amplitude of the angular power spectrum at very small scales. Ultimately, all our analyses serve as a set of consistency tests of the concordance cosmological model, the ΛCDM.