The cosmic web crystal: Ising model for large-scale structures

Abstract

If Dark Matter halos possess the gravitational equivalent of an intrinsic magnetic spin, a formal analogy exists between the low redshift behavior of the Cosmic Web in a flat FLRW background and a crystal of spins submerged in a thermal reservoir with temperature [Formula: see text]. We argue that, within the use of the Bianchi type IX geometry to describe the gravitational collapse of matter inhomogeneities, the spins are nothing but the heritage of its underlying SU(2) symmetry. Therefore, just like electrons in quantum mechanics, these structures may have spin independently from their orbital angular momentum. We explore the phenomenological implications on cosmological scales of a possible late-time phase transition of the Cosmic Web towards (the gravitational equivalent of) a ferromagnetic state, described qualitatively using the Ising model in the mean field approximation.