Cosmology with Quasars

Abstract

We test one of the claims of the Cosmological principle, the one of statistical spatial isotropy. Using a measure of anisotropy based on Shannon Entropy, we calculate anisotropy parameters for selected 3D regions from the Milliquas Dataset, pixel by pixel, by using HEALPix for the tessellation of the sky, and we test how this information entropy based anisotropy changes with transverse and radial distance (distances converted from redshifts using the ΛCDM model with Ω_{m,0} = 0.31, Ω_{Λ,0} = 0.69, and h = 1), and compare the same with isotropic mock datasets generated using Monte Carlo dartboard technique. We also convert the selected regions of the dataset, and the mock distributions into discrete probability distributions, so as to compare the two using Kullback-Leibler Divergence, for both the radial and transverse cases. We find through the transverse analysis that the measure of anisotropy decreases with an increase in the angular bin size, and the radial analysis tells us that the difference between the anisotropy values of real data and those of our isotropic mock data are only about the order of 1e−3, but not attained at the scale of our analysis. The same analysis would make for a fairer comparison if made with a ΛCDM mock catalog instead of the Monte Carlo mock catalogs.