Studies on a New Cosmological Model Based on Complex Metric

In this thesis, the implications of a new cosmological model are studied, which has features similar to that of decaying vacuum cosmologies. Decaying vacuum (or cosmological constant \Lambda) models are the results of attempts to resolve the problems that plague the standard hot big bang model - the problems which elude a satisfactory solution even after the two decades of of inflationary models, the first and much publicised cure to them. We arrive at the present model by a radically new route, which extends the idea of a signature change in the metric, a widely discussed speculation in the current literature. An alternative approach uses some dimensional considerations in line with quantum cosmology and gives an almost identical model. Both derivations involve some fundamental issues in general theory of relativity. The model has a coasting evolution (i.e., a \propto t). It claims the absence of all the aforementioned puzzles in the standard model and has very good predictions. In the first two chapters of the thesis, we review the general theory of relativity, the standard model in cosmology, its successes, the problems in it and also the most successful of those attempts to solve them, namely, the inflationary and decaying vacuum models. In the third chapter, we present and discuss the new cosmological model in detail. The fourth chapter is concerned with quantum cosmology. We briefly review the canonical quantisation programme of solving the Wheeler-DeWitt equation, then apply the procedure to our model and show that it satisfies many of the much sought-after ideals of this formalism. The last chapter of the thesis compares the new model with other ones. It also discusses the appearance of a Casimir type negative energy density in it and the prospects and challenges ahead for the model.