Information Content of the Cosmic Web

TL;DR

This paper introduces an information-theoretic framework analyzing the Cosmic Web's structure using tidal eigenvalues and multifractal entropy, revealing the dominant role of filaments and linking entropy evolution to cosmic growth rates.

Contribution

It extends traditional density-based analyses by incorporating tidal eigenvalues and multifractal entropy, offering new insights into the geometry and evolution of large-scale cosmic structures.

Findings

Filaments are identified as the main information carriers.

Tidal eigenvalue entropy peaks near gravitational saddle points.

Redshift evolution of entropy relates to the linear growth rate f(z).

Abstract

We present an information-theoretic analysis of the Cosmic Web that goes beyond the scalar density contrast and exploits the full structure of the tidal deformation tensor. The three eigenvalues (lambda1, lambda2, lambda3) of the tidal Hessian furnish a natural morphological classifier: clusters, filaments, walls, and voids correspond to (+,+,+), (+,+,-), (+,-,-), and (-,-,-) sign patterns, and their joint probability distribution function (PDF), known analytically in the linear regime from Doroshkevich (1970), defines a continuous Shannon entropy that quantifies the information encoded in the geometry of large-scale structure. Additional information resides in the shear invariants Q = Trace(T2) and A = Trace(T3), which are algebraically independent of the density contrast delta and capture anisotropic deformation invisible to the density alone. The information dimension of each morphological component is related to its Hausdorff (fractal) dimension through the multifractal formalism: clusters (DH = 1.2), filaments (DH = 1.8), walls (DH = 2.5), and voids (DH = 3) define a spectrum of generalized Renyi dimensions Dq, whose q = 1 limit recovers the Shannon information dimension. The resulting entropy budget identifies filaments as the dominant information carriers of the mater distribution, while the tidal eigenvalue entropy is maximized in wall-like configurations near the saddle points of the gravitational potential. We also compute the redshift evolution of the multifractal entropy and derive its relation to the linear growth rate f(z), providing an independent constraint complementary to redshift-space-distortion measurements of f*sigma8.