The Semiclassical Limit of Quantum Cosmology

In this dissertation we have studied how the semiclassical limit of quantum cosmology emerges from a fully quantum mechanical description in terms of a wave function of the universe. Two basic properties defining classical behavior are "decoherence" and "correlations between coordinates and momenta". We discuss how these properties arise for the "relevant" cosmological degrees of freedom as a consequence of interaction with an "environment" consisting of "irrelevant" degrees of freedom. This is studied via a reduced density matrix and Wigner function approach and we also go on to demonstrate how the correlations that define the semiclassical de-cohering histories of the relevant cosmological variables are affected by interaction with the environment. Incorporating the criteria of decoherence and correlation together, we find a set of conditions under which the so-called semiclassical Einstein equations are valid and demonstrate the relation between decoherence and backreaction. We explore these ideas in the context of various minisuperspace cosmological models, paying special attention to non-trivial features that arise in multidimensional minisuperspaces. We relate our results to well-known results in quantum field theory in curved space time and see how decoherence is related to particle production. In the second part of this dissertation we investigate the question of the validity of a minisuperspace approximation as a description of quantum gravity. We try to illustrate this in the example of an interacting (lambda phi^4) field theory in a closed Robertson -Walker Universe. The scale factor and the zero mode of the scalar field simulate the minisuperspace sector and the higher modes of the scalar field mimic the inhomogeneous gravitational degrees of freedom that are truncated in the minisuperspace approximation. We explicitly derive the backreaction of the higher modes on the minisuperspace sector and demonstrate that a minisuperspace description is valid only when this backreaction is small compared to the minisuperspace potential.