| dc.description.abstract | The origin and the nature of the universe has intrigued the human mind since time immemorial. Till the beginning of this century, lack of observational data and the absence of a consistent theory of gravitation had precluded the construction of a realistic model for the universe. A variety of cosmological observations made in the past few decades and the advent of the general theory of relativity have made it meaningful to inquire about the origin and the nature of the universe.
Big Bang cosmology, proposed by Friedmann in the beginning of this century and later developed by Robertson, Walker, Lemaître, Eddington and in recent times by Gamow and others, has come to be accepted as the standard model. In spite of its success, the standard model suffers from several serious predicaments. The initial singularity and the concomitant horizon and flatness problems are the main drawbacks of the model.
In this thesis we shall be interested in constructing nonsingular cosmological models. These models are shown to be devoid of several other problems encountered in the standard model.
In the first chapter a brief review of the standard model is given to set up the notation and to discuss the problems of the model in some detail. The initial singularity is shown to be the root cause of the horizon and the flatness puzzles. The problem of homogeneity and isotropy, the cosmological constant problem and the baryon number problem are also discussed. A qualitative survey of the attempts made by several researchers to overcome the problems of the standard model is presented. The current status of quantum cosmology and the inflationary universe scenario is summarized. The choice of topics in this connection is prejudiced and it is by no means complete. Several important subjects of current interest like Kaluza-Klein models, steady-state cosmology etc., are left out because they are not directly connected with the theme of the thesis. In the closing section of the first chapter, the motivation for the present work is given.
In the beginning of the second chapter a short summary of Dirac cosmology-which happens to be the first model to incorporate a varying gravitational coupling “constant”-is presented. Zee’s broken symmetry theory of gravity and its implications to cosmology are dealt with in sec. 2.2. A scalar field non-minimally coupled to a gravitational field severely affects the “making” of symmetry in the early universe. In contrast to grand unified theories, symmetry breaking is more important for the early universe and symmetry is restored only in the limit of an infinite expansion. As a consequence of this, the gravitational interaction between elementary particles is found to be repulsive in the early epochs. Several models which incorporate these features are discussed towards the end of the second chapter. The ground state field configurations are obtained by extremising the potential and demanding that the extrema be stable. In this sense the analysis carried out in this chapter is heuristic and therefore incomplete.
In Chapter III, a massless scalar field non-minimally coupled to the Friedmann-Robertson-Walker space-time is studied. The ground state solutions to the scalar field equation are obtained in terms of the cosmic scale factor. The resulting symmetry breakdown with its novel features are highlighted. The implications of such solutions for a re-defined gravitational coupling coefficient are enunciated. Vacuum solutions of the scalar field are in turn used to solve the metric field equations. The solutions thus obtained are shown to be nonsingular (for the open universe) by proving (a) the completeness of the null geodesics and (b) the finiteness of the curvature tensor components and the invariants formed out of them.
Non-zero temperature calculations indicate that a scalar field acquires temperature-dependent mass terms. Thus in Chapter IV, the study of a massive scalar field coupled non-minimally to gravity is taken up. Solutions to the scalar field equations are made possible with the assumption that the mass of the scalar field varies inversely with the cosmic scale factor. Under favourable circumstances, symmetry is shown to break down even in closed and flat universes. The presence of a mass term leads to an energy-momentum tensor with a non-zero covariant divergence. To be consistent with the principle of equivalence the total energy-momentum tensor is required to obey the conservation laws. It is shown that the presence of the mass term severely alters the behaviour of ordinary matter and radiation. Finally, solutions to the field equations are obtained and their nonsingular nature is demonstrated.
In the concluding chapter the possibility of further work is explored. | |
