A Study of Homogeneous and Isotropic Cosmological Models

Abstract

Cosmology is the study of universe as a whole. Cosmos means universe and logos means science or study; therefore, the science of universe is known as cosmology. Gravitation can be described by a space-time (metric). The metric is related to the matter and energy in the Universe through Einstein’s field equation, which contains matter as well as energy part. The left-hand side of the Einstein’s field equations is the Einstein’s tensor, which describes the geometry of the Universe. The energy momentum tensor present in the right-hand side of the Einstein’s equations, describes the energy part of the Universe.The Einstein theory is not the only geometric theory of gravitation that can be constructed upon the Newton theory and special relativity. Almost all of the assumptions made in constructing new theories can be modified so that another set of equations will result. In this research work we have investigated Bianchi cosmological models, under the framework of general relativity, and some alternative theories of gravity. In the framework of General Relativity and assuming the Copernican principle, accounted for by the Friedman-Lemaitre-Robertson-Walker metric, a spatially flat universe is consistent with the cosmographic conversely, this condition, which is fulfilled by astrophysical measurements, necessarily requires spatial flatness. Here, we will construct some cosmological models assuming the validity of General Relativity, of Copernican principle (homogeneity and isotropy at large scale) and on dark energy pictured either by some non-ideal fluids or by canonical scalar fields interacting with dark matter. A theorist cannot appeal to this theory in order to justify their views.