Chaotic universe model: Lotka-Volterra dynamics of the universe evolution

Abstract

In this study, we consider nonlinear interactions between components such as dark energy, dark, matter and radiation in the Friedman-Robertson-Walker space-time framework and propose a simple interaction model based on time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra equation for suitable equation of state parameters. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for $0>w_{de}>-1$, $w_{dm}\ge 0$, $w_m\ge 0$ and $w_r\ge 0$ values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in time evolution of the densities. These results imply that the time evolution of the universe is chaotic in the presence of interactions between these components. The present model may has potential to solve some cosmological problems such as the singularity, cosmic coincidence, crunch, big rip, horizon, oscillations, emergence of galaxies, and large scale organization of the universe. Model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe, and offers a new perspective and a different scenario for the universe evolution unlike well known popular models.

9 pages. Figures have been added into the tex

References in corpus (17)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Interacting holographic dark energy model in non-flat universe
• Interacting holographic generalized Chaplygin gas model
• Effects of the interaction between dark energy and dark matter on cosmological parameters
• The behaviour of dark matter associated with 4 bright cluster galaxies in the 10kpc core of Abell 3827
• Testing the viability of the interacting holographic dark energy model by using combined observational constraints
• Turnaround in Cyclic Cosmology
• Cosmological Evolution of Interacting Phantom Energy with Dark Matter
• Interacting Vector-like Dark Energy, the First and Second Cosmological Coincidence Problems
• Interacting models may be key to solve the cosmic coincidence problem
• Testing the interaction between dark energy and dark matter via latest observations
• The imprint of the interaction between dark sectors in large scale cosmic microwave background anisotropies
• Direct Detection Signatures of Self-Interacting Dark Matter with a Light Mediator
• Has DAMA Detected Self-Interacting Dark Matter?
• Scaling Relations of Halo Cores for Self-Interacting Dark Matter
• On the self-interaction of dark energy in a ghost-condensate model

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• Holographic approach for dark energy - dark matter interaction in curved FLRW spacetime
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• Detection of chaos in the general relativistic Poynting-Robertson effect: Kerr equatorial plane
• Protected chaos in a topological lattice
• Non-commutative phase-space Lotka-Volterra dynamics: the quantum analogue
• A holographic cut-off inspired in the apparent horizon
• Qualitative analysis for viscous cosmologies in a non linear regime of the Israel-Stewart formalism
• Role of a periodic varying deceleration parameter in Particle creation with higher dimensional FLRW Universe