A method for testing the cosmic homogeneity with Shannon entropy

Abstract

We propose a method for testing cosmic homogeneity based on the Shannon entropy in Information theory and test the potentials and limitations of the method on Monte Carlo simulations of some homogeneous and inhomogeneous 3D point process in a finite region of space. We analyze a set of N-body simulations to investigate the prospect of determining the scale of homogeneity with the proposed method and show that the method could serve as an efficient tool for the study of homogeneity.

7 pages, 3 figures, Accepted for publication in MNRAS

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• Probing large scale homogeneity and periodicity in the LRG distribution using Shannon entropy
• A new method for testing isotropy with Shannon entropy
• On the complexity and the information content of cosmic structures
• Cosmological homogeneity scale estimates are dressed
• Testing isotropy in the Two Micron All-Sky redshift survey with information entropy
• Relating information entropy and mass variance to measure bias and non-Gaussianity
• How complex is the cosmic web?
• Testing homogeneity of the galaxy distribution in the SDSS using Renyi entropy
• A new method to probe the mass density and the cosmological constant using configuration entropy
• Characterising cosmic inhomogeneity with anomalous diffusion
• Tomography of stellar halos: what does anisotropy in a stellar halo tell us?
• Can the angular scale of cosmic homogeneity be used as a cosmological test?
• A Test for the Zero Mean Hypothesis in Cosmology
• An effective $\mathbf{\Lambda }$-Szekeres modelling of the local Universe with Cosmicflows-4