The Einstein static universe in the Gauss-Bonnet extention of teleparallel theories

Abstract

The purpose of this dissertation is to examine the stability of the Einstein Static Universe (ESU) in some cases of the f (T, Tc;) gravity model. Using the teleparallel equivalent of general relativity, the invariants of the torsion term, T and the teleparallel equivalent of Gauss-Bonnet term, Tc were introduced along with the f(T, Tc) model. This model represents an alternative to the dark energy and dark matter quantities and is of the quartic order of the contorsion term. The evolution of the ESU was studied in 7 specific cases of the f (T, To) model by imposing linear scalar perturbations of the scale factor, the density and pressure parameters in the Friedman equations of each case. Additionally, the equation of state of a perfect fluid, p = wp, has been considered. The results were unique for each scenario showing that in 4 cases the growth of the perturbed scale factor is exponential, where the rest 3 cases do not have an analytical solution.