The Jungle Universe: coupled cosmological models in a Lotka–Volterra framework

Abstract

In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann–Lemaître universes is a special case of generalized Lotka–Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka–Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann–Lemaître cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserves the structure of the dynamical equations. Using the standard tools of Lotka–Volterra dynamics, we obtain the general Lyapunov function of the system when one of the fluids is coupled to dark energy. This provides in a rigorous form a generic asymptotic behavior for cosmic expansion in presence of coupled species, beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, we conjecture that chaos can appear for at least four interacting fluids.