A Study of Evolution of Cosmological Parameters Based on Dark Energy Models in Kaluza-Klein Framework

Abstract

The purpose of the present study is to determine the characteristics of time evolution of various cosmological quantities, based on four models constructed for a universe undergoing accelerated expansion. This formulation is done in the framework of Kaluza-Klein space-time, for zero spatial curvature. To solve the field equations, an ansatz is chosen for each model in such a way that it leads to a signature flip of the deceleration parameter, to ensure its consistency with recent astrophysical observations indicating a change from a decelerated expansion to an accelerated expansion of the universe. Based on these four models, time evolutions of several cosmological parameters are obtained and their variations are shown graphically against time. The arbitrary constants, associated with each model, are so tuned that the model correctly predicts the values of the Hubble parameter, deceleration parameter, energy density and gravitational constant at the present time. The findings from these models are consistent with each other, and they are in agreement with the observed features. The gravitational constant (G) shows a rapid fall in the early universe, followed by an extremely slow rise which continues at the present time. Taking (G) as a constant in two of the four models, the cosmological constant is found to be independent of time. A significant finding is that the signature flip of the deceleration parameter almost coincides with the signature flip of the cosmological constant (Λ), pointing towards a relation between the accelerated expansion and the dark energy which is represented by Λ. Other plots with respect to Λ also depict dark energy’s role in governing cosmic evolution. Considering its dynamical nature, Λ is referred to as cosmological term (instead of cosmological constant) in the text. Contrary to the common trend of using arbitrary units, the SI units for all measurable quantities are used.