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

Understand

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 $250 \, h^{-1}\, {\rm Mpc}$.