The Cosmic Web Crystal: Ising model for Large Scale Structures

TL;DR

This paper proposes an analogy between the large-scale structure of the universe and a magnetic spin system, suggesting that cosmic web structures may undergo phase transitions similar to ferromagnetism, modeled via the Ising model.

Contribution

It introduces a novel analogy linking cosmic web structures to spin systems and explores potential phase transitions using the Ising model in a cosmological context.

Findings

Analogous behavior between cosmic web and spin systems identified

Potential for late-time phase transition in cosmic structures proposed

Implications for understanding large-scale structure evolution discussed

Abstract

If Dark Matter halos possess the gravitational equivalent of an intrinsic magnetic spin, a formal analogy exists between the low redshift behaviour of the Cosmic Web in a flat FLRW background, and a crystal of spins submerged in a thermal reservoir with temperature $T \propto H(t)$. 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.