Lyra cosmologies with the dynamical system perspective

Abstract

In this study, we revisit the homogeneous and isotropic, spatially curved model in the Lyra geometry framework. We apply the dynamical system approach to study the universe evolution in model. The present cosmic dynamical system formulation is independent of the model parameter which yields the universe expansion phases dominated by the stiff fluid, radiation, dark matter and dark energy. These expansion phases in the Lyra model are consistent with the General relativity model. In addition, the displacement vector field of the Lyra geometry model will give rise to the stiff matter dominated phase during early times of the universe evolution. The cosmographic parameters, EoS parameter and statefinder diagnostic have been utilized in the dynamical system to illustrate the cosmic evolution of the universe. The numerical solution technique is used to illustrate graphical behaviors of the cosmological parameters. On the basis of dynamical system and numerical analysis, we exhibit that the model explains accelerating universe expansion with transition from the decelerating phase and it will lead to the $\Lambda$ cold dark matter ($\Lambda$CDM) model in the near future.