Isochronous cosmological solutions of the Friedmann–Robertson–Walker model

Abstract

In this paper, the periodic solutions of the equation of Friedmann–Robertson–Walker cosmology with a cosmological constant are investigated. Using variable transformation, the original second-order ordinary differential equation is converted to a planar dynamical system with cosmic time t. Numerical simulations indicate that period function T(h) of this dynamical system is monotonically increasing. However, a new planar dynamical system could be deduced by using conformal time variable [Formula: see text]. We prove that the new planar dynamical system has two isochronous centers under certain parameter conditions by using Picard–Fuchs equation. Explicitly, we find that there exist two families of periodic solutions with equal period for the new planar dynamical system which is derived from the Friedmann–Robertson–Walker model.

The Friedmann Robertson Walker Space time in Lyra Geometry

“…For is time dependent and is constant, from (8) we get: (11) where is a constant. The deceleration parameter is given by: (12) where is the average scale factor and reads as: (13) From ( 12) we get: (14) By comparing ( 13) and ( 14) we can take: (15) where , and are constants. From ( 5) and ( 6) we get:…”

“…Holden et al [12] presented a phase-plane analysis of FRW cosmologies in Brans-Dicke gravity. Isochronous cosmological solutions of the FRW model were investigated by Chen et al [13]. Aref'eva et al [14] studied dynamics in nonlocal linear models in the FRW metric.…”