Periodic solutions with equal period for the Friedmann–Robertson–Walker model

Abstract

In this letter, we study the periodic solutions of the equation of barotropic Friedmann–Robertson–Walker cosmologies. Using variable transformation, the original second order ordinary differential equation is converted to a planar dynamical system. We prove that the planar dynamical system has two isochronous centers under certain parameter conditions by using Picard–Fuchs equation. Consequently, we find that there exist two families of periodic solutions with equal period for the Friedmann–Robertson–Walker model.