Vacuum dynamics in the early universe scenarios of phase transitions and extra dimensions

Understanding the origin of the physical processes that evolved and gave rise to the universe we observe today becomes one of the most important and challenging questions in cosmology. Thus the vacuum structure of the early universe and its dynamics responsible for evolving it to present remains an outstanding and fascinating problem for the understanding of our universe. In this work we investigate some of the questions related to the dynamics and vacuum phase structure in the cosmological setting of the early universe, by analyzing two scenarios, namely; tunneling and the 5-dimensional Randall Sundrum(RS) model.;In the first part of this thesis we investigate the nonlinear dynamics of tunneling and its relation to the consequent particle creation, both arising from vacuum fluctuations in 4-dimensions. A detailed analysis of the relation between the excitations of the field about the true vacuum (interpreted as particle creation) and the phase shift coming from tunneling is presented. Further, we extend our result on resonant tunneling and consequent particle creation to the case of finite temperature.;In the second part of this thesis we analyze the following cosmological aspects of the 5-dimensional Randall-Sundrum model, (a) The effect of the global 5-D space-time topology on the stability of the allowed field configurations on the 3-brave. (b) An extension of the RS model to the case of many (and) inflating branes whose dynamics can induce an effective 4-dimensional cosmological constant, Λ. (c) Further, we addressing the moduli problem in the extended scenario, in order to ensure stability of the whole 5-dimensional setup and reconcile this model with conventional FRW cosmology and astrophysical constraints, at late times (but before BBN).;We examine the cosmology of the Randall-Sundrum (RS) model in a dynamic setting where scalar fields are present in the bulk as well as the branes. The model recovers the radiation dominated FRW universe. (Abstract shortened by UMI.)...