| Inspired by recent evidence for a positive cosmological constant, this thesis considers some of the implications of trying to incorporate approximately seventy percent of the universe, namely dark energy, consistently into quantum field theory on a curved background. Such considerations may have implications for inflation, the understanding of dark energy at the present time and finally the challenging topic of trying to incorporate a positive cosmological constant into string theory. We will mainly examine various aspects of the one parameter family of de Sitter invariant states---the so called alpha-vacua. On the phenomenological side, not only could such states provide a window into trans-planckian physics through their imprint on the cosmological microwave background (CMB), but they may also be a source of ultra-high energy cosmic rays (UHECR) at the present time. From a purely theoretical perspective, formulating interacting quantum field theory in these states is a challenging problem which we consider in quite some detail.; Inflation solves many of the outstanding problems inherent to the standard model of cosmology. It also introduces the tantalizing possibility that we may be able to extract information about physics at the planckian scale. During inflation, sub-planckian scales expand to macroscopic size, suggesting that there might be an observable cosmological imprint of planckian scale physics. This trans-planckian "window of opportunity" is one of the few ways that we may be able to probe these scales (which may be governed by stringy physics) using present technology.; One way of modeling trans-planckian effects is to consider the alpha-vacua. Modeling slow-roll inflation as a transition between states with two different cosmological Constants, we found that one is required to take alpha << H/M to prevent excessive particle production at the end of inflation. Here H is the Hubble constant and M is some proper momentum scale cutoff. Give these constraints we find that there may indeed be effects on the CMB.; While it was clear that there may be observable effects on the CMB, objections were raised about the theoretical consistency of the physics of these vacua. It was suggested that there were problems with renormalizability, locality, causality, and stability for these vacua. To address these issues we sought to formulate the field theory using an imaginary-time technique. Geometrically, this corresponds to considering field theory on the euclidean section of de Sitter space which is a sphere. We found that the theory was renormalizable with local counter-terms, and that at one-loop the renormalized stress-energy tensor was real, suggesting stability. (Abstract shortened by UMI.)... |
