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

Jérome Perez, André Füzfa, Timoteo Carletti, Laurence Melot, Sêcloka Lazare Guedezounme

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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.
Original languageEnglish
Article number46
Pages (from-to)1753
Number of pages23
JournalGeneral Relativity and Gravitation
Volume46
Issue number4
DOIs
Publication statusPublished - 1 May 2014

Keywords

  • Cosmology
  • Coupled models
  • Dynamical systems
  • Dark energy
  • Predator-prey system

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  • Projects

    PAI n°P7/19 - DYSCO: Dynamical systems, control and optimization (DYSCO)

    WINKIN, J., Blondel, V., Vandewalle, J., Pintelon, R., Sepulchre, R., Vande Wouwer, A. & SARTENAER, A.

    1/04/1230/09/17

    Project: Research

    Student Theses

    The Jungle Universe

    Author: Melot, L., 30 Jun 2012

    Supervisor: Fuzfa, A. (Supervisor) & Pérez, J. (External person) (Co-Supervisor)

    Student thesis: Master typesMaster in Mathematics

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