Friedmann equations as n-dimensional dynamical system

Abstract

In this paper we study dynamics of the standard cosmological model of the universe assuming that it is filled with n types of non-interacting barotropic perfect fluids. For that purpose, a dynamical system of a class of Lotka-Volterra dynamical systems is derived, that consists of n nonlinear differential equations of the first order, whose dependent variables are density parameters of the material in the universe. Analytical solution of that system represents new parametrization of density parameters. Moreover, we perceive the evolution of the universe in the frame of the linear stability theory.

Keywords

• friedmann equations
• lotka-volterra equations
• cdm model
• nonlinear differential equations
• dynamical systems
• primary 34a34, 37n99
• secondary 83f05