Certain Investigation On Spherically Symmetric Cosmological Model in General Relativity

In this paper, we have presented a spherically symmetric a cosmological model in general relativity with the help of Lyra’s geometry with time dependent displacement field. The Lyra’s geometry which is a generalization of Weyl’s geometry (removing the defect of non-integrability of length transfer). gravitational theory and the cosmology based on this geometry have been reviewed. Exact solutions have been obtained for constant deceleration parameter models of the universe. Further, cosmological models with both constant and time dependent displacement field have been discussed. We discuss a model universe with different situations, by solving the modified Einsteinfield equation within the framework of Lyra geometry, specially for Non-flat models. This model is suitable for an early stage of the universe, that is, before the universe underwent the compactification transition. The explicit solution of the scale factor are found via the assumption of an equation of state p=Υ ρ, where Υ=0.5. varies cases have been considered. When the space-time dimension N = 4, our solution reduces to that of Singh and Desikan. Some physical properties of the models are also discussed.