Disordered hyperuniform modulated phases and the cosmic web from one free energy

Abstract

Disordered hyperuniformity spans twenty-five orders of magnitude, from the microscopic world of soft and condensed matter to the distribution of matter in the universe. We introduce a free-energy functional with no adjustable coupling, a phase-field-crystal ordering term and a Newtonian tail, and show that its two kinetic limits generate two of these structures. Under conserved overdamped dynamics it arrests in a bicontinuous labyrinth of the kind found in confined fluids, block copolymers, active matter and vegetation patterns, which is a class III disordered hyperuniform state; under inertial dynamics in an expanding background it generates a cosmic web whose tidal skeleton matches that of gravity alone to within $0.03$ in every morphological class. In both limits the suppressed long-wavelength fluctuations are inherited from the initial condition rather than made by the dynamics: the large-scale exponent of the arrested state equals the primordial one, and gravity rescales the infrared spectrum by the linear growth factor to better than one per cent over a factor $1363$ of growth. The two sectors are continuously connected, and their distance is measurable: once the ordering modulation saturates, its mean-field back-reaction leaves the medium with a residual pressure proportional to $λ_0^2$ that suppresses the growth of the largest scales by a smooth factor and vanishes in the cold-matter limit $λ_0\to0$.