Abstract:
This memory with relativistic cosmology at large scales, in flat universe.
The manuscript begins with an introduction followed by three chapters and ended with a conclusion.
In the introduction, the motivation of our work is given together with the organization of manuscript.
The first chapter is an introduction to relativistic cosmology. We deal with homogeneous and isotropic universe. The assumption that the universe is homogeneous and isotropic leads us to choose the space-time coordinate system so that the metric takes a simple forme, called Robertson-Walker
metric. We applied the Einstein equations to the Robertson-Walker metric, and derived some of the basic results that are needed here in this manuscript.
The second chapter concentrates on the small departures from homogeneity and isotropy.
We applied the Einstein equations to the perturbed Robertson-Walker metric, we derived the equation governing growth of density perturbations in the matter, assuming all other components of universe smooth.
The growth rate of matter perturbations can be used to distinguish between dark energy and modified gravity at cosmological scales as explanation to the observed cosmic acceleration.
The growth rate is parametrized by a growth index The last chapter deals with parametrization of the growth index, using Mocker model for early dark energy. We found simple expression for gama as function od the dimensionless matters density and the equation of state w of of the early dark energy. The parametrization covering low intermediate and high redshifts up to ZCMBat the decoupling epoch. The parametrization Fit very well the growth factor. The fit is better than 0.5%
