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

Research output: Contribution to journalArticle

143 Downloads (Pure)

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

Fingerprint

tropical regions
universe
fluids
Liapunov functions
dark energy
chaos
formulations
expansion

Keywords

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

Cite this

@article{d2de57c8b59f434d82a14018d926b53a,
title = "The Jungle Universe: coupled cosmological models in a Lotka–Volterra framework",
abstract = "In this paper, we exploit the fact that the dynamics of homogeneous andisotropic Friedmann–Lema{\^i}tre universes is a special case of generalized Lotka–Volterra system where the competitive species are the barotropic fluids filling theUniverse. Without coupling between those fluids, Lotka–Volterra formulation offersa pedagogical and simple way to interpret usual Friedmann–Lema{\^i}tre cosmologicaldynamics. A natural and physical coupling between cosmological fluids is proposedwhich preserves the structure of the dynamical equations. Using the standard toolsof Lotka–Volterra dynamics, we obtain the general Lyapunov function of the systemwhen one of the fluids is coupled to dark energy. This provides in a rigorous forma generic asymptotic behavior for cosmic expansion in presence of coupled species,beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, weconjecture that chaos can appear for at least four interacting fluids.",
keywords = "Cosmology, Coupled models, Dynamical systems, Dark energy, Predator-prey system, dynamical systems, cosmology, population dynamics",
author = "J{\'e}rome Perez and Andr{\'e} F{\"u}zfa and Timoteo Carletti and Laurence Melot and Guedezounme, {S{\^e}cloka Lazare}",
year = "2014",
month = "5",
day = "1",
doi = "10.1007/s10714-014-1753-8",
language = "English",
volume = "46",
pages = "1753",
journal = "General Relativity and Gravitation",
issn = "0001-7701",
publisher = "Springer New York",
number = "4",

}

TY - JOUR

T1 - The Jungle Universe: coupled cosmological models in a Lotka–Volterra framework

AU - Perez, Jérome

AU - Füzfa, André

AU - Carletti, Timoteo

AU - Melot, Laurence

AU - Guedezounme, Sêcloka Lazare

PY - 2014/5/1

Y1 - 2014/5/1

N2 - In this paper, we exploit the fact that the dynamics of homogeneous andisotropic Friedmann–Lemaître universes is a special case of generalized Lotka–Volterra system where the competitive species are the barotropic fluids filling theUniverse. Without coupling between those fluids, Lotka–Volterra formulation offersa pedagogical and simple way to interpret usual Friedmann–Lemaître cosmologicaldynamics. A natural and physical coupling between cosmological fluids is proposedwhich preserves the structure of the dynamical equations. Using the standard toolsof Lotka–Volterra dynamics, we obtain the general Lyapunov function of the systemwhen one of the fluids is coupled to dark energy. This provides in a rigorous forma generic asymptotic behavior for cosmic expansion in presence of coupled species,beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, weconjecture that chaos can appear for at least four interacting fluids.

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

KW - Cosmology

KW - Coupled models

KW - Dynamical systems

KW - Dark energy

KW - Predator-prey system

KW - dynamical systems, cosmology, population dynamics

U2 - 10.1007/s10714-014-1753-8

DO - 10.1007/s10714-014-1753-8

M3 - Article

VL - 46

SP - 1753

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

SN - 0001-7701

IS - 4

M1 - 46

ER -