The small-scale environment characterized by the local density is known to play a crucial role in deciding the galaxy properties but the role of large-scale environment on galaxy formation and evolution still remain a less clear issue. We propose an information theoretic framework to investigate the influence of large-scale environment on galaxy properties and apply it to the data from the Galaxy Zoo project which provides the visual morphological classifications of ∼ 1 million galaxies from the Sloan Digital Sky Survey. We find a non-zero mutual information between morphology and environment which decreases with increasing length scales but persists throughout the entire length scales probed. We estimate the conditional mutual information and the interaction information between morphology and environment by conditioning the environment on different length scales and find a synergic interaction between them which operates upto at least a length scales of ∼ 30 h −1 Mpc. Our analysis indicates that these interactions largely arise due to the mutual information shared between the environments on different length scales.

We analyze a set of volume limited samples from SDSS DR12 to quantify the degree of inhomogeneity at different length scales using Shannon entropy. We find that the galaxy distributions exhibit a higher degree of inhomogeneity as compared to a Poisson point process at all length scales. Our analysis indicates that signatures of inhomogeneities in the galaxy distributions persist at least upto a length scale of 120 h −1 Mpc. The galaxy distributions appear to be homogeneous on a scale of 140 h −1 Mpc and beyond. Analyzing a set of mock galaxy samples from a semi analytic galaxy catalogue from the Millennium simulation we find a scale of transition to homogeneity at ∼ 100 h −1 Mpc.

We quantify the degree of inhomogeneity in the Luminous Red Galaxy (LRG) distribution from the SDSS DR7 as a function of length scales by measuring the Shannon entropy in independent and regular cubic voxels of increasing grid sizes. We also analyze the data by carrying out measurements in overlapping spheres and find that it suppresses inhomogeneities by a factor of 5 to 10 on different length scales. Despite the differences observed in the degree of inhomogeneity both the methods show a decrease in inhomogeneity with increasing length scales which eventually settle down to a plateau at ∼ 150 h −1 Mpc. Considering the minuscule values of inhomogeneity at the plateaus and their expected variations we conclude that the LRG distribution becomes homogeneous at 150 h −1 Mpc and beyond. We also use the Kullback-Leibler divergence as an alternative measure of inhomogeneity which reaffirms our findings. We show that the method presented here can effectively capture the inhomogeneity in a truly inhomogeneous distribution at all length scales. We analyze a set of Monte Carlo simulations with certain periodicity in their spatial distributions and find periodic variations in their inhomogeneity which helps us to identify the underlying regularities present in such distributions and quantify the scale of their periodicity. We do not find any underlying regularities in the LRG distribution within the length scales probed.

We analyze two volume limited galaxy samples from the SDSS photometric and spectroscopic data to test the isotropy in the local Universe. We use information entropy to quantify the global anisotropy in the galaxy distribution at different length scales and find that the galaxy distribution is highly anisotropic on small scales. The observed anisotropy diminishes with increasing length scales and nearly plateaus out beyond a length scale of 200 h −1 Mpc in both the datasets. We compare these anisotropies with those predicted by the mock catalogues from the N-body simulations of the ΛCDM model and find a fairly good agreement with the observations. We find a small residual anisotropy on large scales which decays in a way that is consistent with the linear perturbation theory. The slopes of the observed anisotropy converge to the slopes predicted by the linear theory beyond a length scale of ∼ 200 h −1 Mpc indicating a transition to isotropy. We separately compare the anisotropies observed across the different parts of the sky and find no evidence for a preferred direction in the galaxy distribution.

We analyze a set of volume limited samples from the SDSS to study the dependence of galaxy colour on different environments of the cosmic web. We measure the local dimension of galaxies to determine the geometry of their embedding environments and find that filaments host a higher fraction of red galaxies than sheets at each luminosity. We repeat the analysis at a fixed density and recover the same trend which shows that galaxy colours depend on geometry of environments besides local density. At a fixed luminosity, the fraction of red galaxies in filaments and sheets increases with the extent of these environments. This suggests that the bigger structures have a larger baryon reservoir favouring higher accretion and larger stellar mass. We find that the mean colour of the red and blue populations are systematically higher in the environments with smaller local dimension and increases monotonically in all the environments with luminosity. We observe that the bimodal nature of the galaxy colour distribution persists in all environments and all luminosities, which suggests that the transformation from blue to red galaxy can occur in all environments.