2026/05/31 by Juan Garcia-Bellido · 1 citation
Physics and Astronomy · #astro-ph.CO #astro-ph.GA
15 pages, 4 figures, to appear in Physics of the Dark Universe
arxiv created 2026/08/02 · arxiv updated 2026/08/04
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 (λ1, λ2, λ3) 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 \cal Q = \rm Tr(T2) and \cal A = \rm Tr(T3), independent of the density. We derive the \it Log-Doroshkevich distribution, and show the ℤ2 symmetry survives the nonlinear map, broken only in matter fractions. Gravitational collapse breaks it through the density skewness: an Edgeworth treatment gives the cluster--void asymmetry R\rm cv-1=0.609 ε3 and entropy difference ΔH\rm CV=0.107 ε3 bits, with ε3=S3\rm tot(R) σ0(R) D(z). The total skewness combines a gravitational term S3\rm grav=34/7+n\rm eff(R) and a primordial one S3\rm PNG=S3(1)(R) f\rm NL with S3(1)(8 h-1\rm Mpc)≃3×10-4, smaller by four to five orders of magnitude, so the one-point asymmetry is gravity-dominated and only weakly sensitive to f\rm NL. The multifractal entropy rate obeys H\rm mf(z)=-3f(z)/(1+z), a growth probe complementary to fσ8.