Investigations on certain cosmological models of general theory of relativity for existence of dark matter in the universe due to variable constants

Abstract

The main objective of the thesis is to construct and analyse some suitable cosmological models along with numerous cosmological consequences with Dark Matter in the universe on the basis of the field equations governing the gravity as proposed by Berman and Rahman et al. recently. This thesis is divided in ten chapters. In Chapter-1, Theory of Cosmology has been discussed along with cosmology time line, Mathematical discovery of the universe, theory of variable G and variable and#923; with observational constraints. In the last section world-metric and linkage between evolutions scenario of cosmological model and space curvature is given. In 1915, Einstein proposed his General theory of Relativity (GTR) governing the gravity. He applied this theory to study the universe as a whole. For this he determined the space time metric which represents the universe as a whole. This model of universe is well known as Einstein s static model. For the construction of static model of the universe, the original form of the field equation of GTR is not suitable and therefore, Einstein introduced the cosmological term ij g L into his field equation calling it as Biggest blunder of my life . After the Hubble s experiments, a number of cosmological models have been constructed by many cosmologists with and without the cosmological term ij g L by taking positive sign of the cosmological constant (C.C.) or even its non-zero numerical value in general. In the same time those cases where the constant is nonzero, have mathematical interest more rather than the physical meaning. The spontaneous symmetry breaking results in a change in the temperature of the medium. This implies a dependence of the cosmological constant on time as may be seen in many cosmological models (discussed in detail in the thesis). In 1961, Brans and Dicke proposed the possibility of the existence of a long-range scalar field on the basis of the Mach s principle. This lead to propose that the constant of Gravitation G is not a constant