An information theory based search for homogeneity on the largest accessible scale

TL;DR

This study uses information theory to analyze the SDSS DR12 quasar catalogue, demonstrating that quasar distribution becomes homogeneous beyond approximately 250 Mpc/h, aligning with expectations for a Poisson process.

Contribution

It introduces an information theory-based method to quantify large-scale homogeneity in quasar distributions, providing new insights into cosmic structure.

Findings

Inhomogeneity decreases with scale and plateaus at ~250 Mpc/h.

Residual inhomogeneity matches Poisson process expectations.

Quasar distribution is homogeneous beyond 250 Mpc/h.

Abstract

We analyze the SDSS DR12 quasar catalogue to test the large-scale smoothness in the quasar distribution. We quantify the degree of inhomogeneity in the quasar distribution using information theory based measures and find that the degree of inhomogeneity diminishes with increasing length scales which finally reach a plateau at $\sim 250 \, h^{-1}\, {\rm Mpc}$. The residual inhomogeneity at the plateau is consistent with that expected for a Poisson point process. Our results indicate that the quasar distribution is homogeneous beyond length scales of $250 \, h^{-1}\, {\rm Mpc}$.