A Dynamical Study of the Friedmann Equations

Abstract

Cosmology is an attracting subject for students but usually difficult to deal with if general relativity is not known. In this article, we first recall the Newtonian derivation of the Friedmann equations which govern the dynamics of our universe and discuss the validity of such a derivation. We then study the equations of evolution of the universe in terms of a dynamical system. This sums up the different behaviors of our universe and enables to address some cosmological problems.

Needs IOP LaTeX class; 17 pages, 9 figures

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Cited by in corpus (17)

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• Introduction to the application of the dynamical systems theory in the study of the dynamics of cosmological models of dark energy
• The Jungle Universe
• The flatness problem and $\Lambda$
• Friedmann-like universes with weak torsion: a dynamical system approach
• Rindler Modified Schwarzschild Geodesics
• How Problematic is the Near-Euclidean Spatial Geometry of the Large-Scale Universe?
• Scalar field cosmology in phase space
• Qualitative study of perfect-fluid Friedmann-Lema\^ıtre-Robertson-Walker models with a cosmological constant
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Big Bang Nucleosynthesis Constraints on the Self-Gravity of Pressure
• Geodesic Motions near an improved Schwarzschild black hole
• Integration of the Friedmann equation for universes of arbitrary complexity
• Particle motion in the field of a five-dimensional charged black hole
• The geodesics structure of Schwarzschild electromagnetic black hole
• Kinematical and dynamical aspects of ghost-matter cosmologies
• Percolation of 'Civilisation' in a Homogeneous Isotropic Universe