THE SPECIAL LAW OF VARIATION FOR HUBBLE'S PARAMETER IN COSMOLOGICAL MODELS AND THE PRESENT UNIVERSE

Abstract

The current study mainly deals with the development and establishment of some mathematical cosmological models for interpretation of the origins and evolution of the universe according to modern observations. In the present work, some current cosmological models are investigated and developed in such a way that would help to predict the physical behavior of the universe in the distant future. The thesis consists of four chapters, 52 figure, 24 tables and ends with a list of references. CHAPTER I briefly reviews three geometric structures. The first structure is Riemannian geometry by means of which the field equations are described in general relativity theory, as well as geodesic equations. Also, a brief summary of the Raychaudhuri equation is presented. The second structure is Absolute parallelism space (AP-Space). The third one is the Parameterized absolute parallelism geometry by means of which it was possible to deduce the modified Raychaudhuri equation which will be used to study the singularity of the cosmological models in chapter IV. At the end of chapter I, a brief review of some of the previous cosmological models that appeared before 1998 and after 1998 is outlined. CHAPTER II proposes two cosmological models which can explain the evolution of the universe after the Big Rip moment. The first model is the periodic universe with a varying deceleration parameter of the second degree of cosmic time, according to which the universe passes through the Big Rip and then retreats as it was at the beginning. According to this model, a closed, flat, and open universe is allowed. The second model is generated by utilizing a varying deceleration parameter as a polynomial of degree l 1 in the cosmic time. The Milne model, the Radiation model, the Einstein-de Sitter model and the Einstein model are concluded as a special case at

(l 1) . The linearly varying deceleration parameter model is obtained at

(l 2) .

Also, the periodic universe with a varying deceleration parameter of the second degree model is found at (l 3) . This model covers all of the previous models and covers the periodic models at

(l 3) . From the previous analysis of the varying

polynomial deceleration parameter, one can observe that by increasing the degree of the deceleration parameter, a periodic multi-stage universe can be obtained. It starts with the Big Bang, passes through the Big Rip, and then retracts to its first state in a repeated operation. Further the universal model PUVDP is compared with LVDP,

PVDP, CDP and CDM models. CHAPTER III constructs a gravitational field with torsion by using the parameterized absolute parallelism geometry. Under the influence of the gravitational field with torsion, the cosmological models are obtained and discussed. It is to be noted that the torsion term leads to inflationary cosmological models with a constant deceleration parameter. We suggest a special law for the deceleration parameter to study the big rip model. The closed and open models turn out to be impossible since the condition of the energy density is unreliable, whereas the flat model is