An information-theoretic bound on cosmic coherence in finite-volume simulations

TL;DR

This paper uses mutual information to measure the maximum scale of coherent cosmic structures in finite-volume simulations, revealing a scale-dependent limit on cosmic coherence relevant for homogeneity analysis.

Contribution

It introduces an information-theoretic approach to quantify cosmic memory and identifies the scale at which cosmic structures lose coherence in simulations.

Findings

Mutual information peaks near one-eighth of the simulation box size.

The coherence scale is robust across different box sizes and discretizations.

Establishes a finite-volume limit on cosmic structure coherence.

Abstract

We quantify the physical memory of the cosmic density field using mutual information between $N$-body snapshots at different redshifts, removing a random baseline to isolate gravitational correlations. The shared mutual information rises with scale, peaks near $\simeq L/8$ (where $L$ is the simulation box size), and declines thereafter. This behaviour is robust to box size and discretization, and identifies the largest coherently retained modes unaffected by missing long-wavelength power, establishing a finite-volume limit on the coherence of cosmic structure with direct implications for homogeneity studies.