Impact of Large-Scale Structure Formation on the Global Information Budget

TL;DR

This paper develops a theoretical framework to quantify how large-scale structure formation impacts the universe's information content, revealing a tiny entropy reduction and exploring implications for cosmic homogeneity and structure growth.

Contribution

It introduces a novel analytical approach to measure the information content evolution due to structure formation and applies it to observational data, connecting entropy changes with cosmological parameters.

Findings

A 0.004% decrease in cosmic information entropy due to structure formation.

The universe's accelerated expansion counteracts entropy growth from structure formation.

No universal scale of homogeneity below 130 h^{-1} Mpc found in SDSS DR18 data.

Abstract

This paper offers an original theoretical framework to quantify the information content associated with cosmological structure formation. By taking into account the growth in perturbations for the matter density field, we are able to calculate the relative reduction in the information entropy from the projection for a fully homogeneous setting. An analytical study is carried out to track back the evolution of global information content up to $z=20$, where a log-normal density distribution with redshift-dependent variance, skewness, and kurtosis is used to mimic the observable Universe. We report a $0.004\%$ drop in the information entropy of the Universe, that is caused by the formation of large-scale structures in the present universe. The accelerated expansion of the Universe is suspected as a countermeasure by nature to override the exponential growth in this entropic drop. We also analyse how the scale factor, expansion rate and growth rate of structure formation are connected with the entropic drop, taking the $\Lambda CDM$ model into account. The formalism is further developed and employed to study the spectrum of information underlying the galaxy distribution in the observable Universe. Using data from SDSS DR18 we also quantify the information sharing across different parts of the studied volume. An attempt to validate the assumption of cosmic homogeneity is made, which rules out the presence of a Universal scale of uniformity below 130 $h^{-1}$ Mpc.