Topics in Inflationary Cosmologies

In this thesis we discuss several aspects of inflationary cosmologies. The first chapter is an introduction to the standard hot big bang cosmological model. We review the model and some of the problems associated with it. In the second chapter, a short review of the proposals for solving the cosmological conundrums of the big bang model is presented. We study the old and the new inflationary scenarios and show why they are not acceptable. Some alternative scenarios especially those using supersymmetry are reviewed briefly. The third chapter is a study of inflationary models where the same set of fields that breaks supersymmetry is also responsible for inflation. In these models, the scale of supersymmetry breaking is related to the slope of the potential near the origin and can thus be kept low. We find that we can get a supersymmetry breaking scale of the order of the weak breaking scale. The cosmology obtained from the simplest of such models is discussed in detail and we find that there are no particular problems except a low reheating temperature and a violation of the thermal constraint. We then present a possible solution to the thermal constraint problem by introducing a second field and discuss the role played by this second field in the scenario. In the fourth chapter, an alternative mechanism for the generation of baryon number within the framework of supergravity inflationary models is studied. We use the gravitational couplings of the heavy fields with the hidden sector (the sector which breaks supersymmetry). This mechanism is applied to two specific models--one with and one without supersymmetry breaking. We emphasize the complete generality of this mechanism. The baryon to entropy ratio is found to be dependent on parameters which are model dependent. Finally, we remark on the effect of direct couplings between the two sectors on our results.