Testing isotropy in the Universe using photometric and spectroscopic data from the SDSS

We analyse two volume limited galaxy samples from the Sloan Digital Sky Survey 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 data sets. We compare these anisotropies with those predicted by the mock catalogues from the N-body simulations of the Λ cold dark matter 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.