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

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 $ΛCDM$ 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.