Theory of Cosmological Perturbations and Applications to Superstring Cosmology

The theory of cosmological perturbations is the main tool which connects theories of the early universe (based on new fundamental physics such as string theory) with cosmological observations. In these lectures, I will provide an introduction to this theory, beginning with an overview of the Newtonian theory of fluctuations, moving on to the analysis of fluctuations in the realm of classical general relativity, and culminating with a discussion of the quantum theory of cosmological perturbations. I will illustrate the formalism with applications to inflationary cosmology. I will review the basics of inflationary cosmology and discuss why - through the evolution of fluctuations - inflation may provide a way of observationally testing Planck-scale physics.Comment: Writeup of lectures delivered at the 2004 Cargese Summer School on String Theory, 49 pages, 3 figure

Infrared effects in inflationary correlation functions

In this article, I briefly review the status of infrared effects which occur when using inflationary models to calculate initial conditions for a subsequent hot, dense plasma phase. Three types of divergence have been identified in the literature: secular, "time-dependent" logarithms, which grow with time spent outside the horizon; "box-cutoff" logarithms, which encode a dependence on the infrared cutoff when calculating in a finite-sized box; and "quantum" logarithms, which depend on the ratio of a scale characterizing new physics to the scale of whatever process is under consideration, and whose interpretation is the same as conventional field theory. I review the calculations in which these divergences appear, and discuss the methods which have been developed to deal with them.Comment: Invited review for focus section of Classical & Quantum Gravity on nonlinear and nongaussian perturbation theory. Some improvements compared to version which will appear in CQG, especially in Sec. 2.3. 30 pages + references

Quantum Brownian Motion in a Bath of Parametric Oscillators: A model for system-field interactions

The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes like decoherence, dissipation, particle creation, noise and fluctuation. We treat the case where the Brownian particle is coupled linearly to a bath of time dependent quadratic oscillators. While the bath mimics a scalar field, the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode or the scale factor of the universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients. This method enables one to trace the source of statistical processes like decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origin of quantum noise and thermal radiance from black holes and from uniformly- accelerated observers in Minkowski space as well as from the de Sitter universe discovered by Hawking, Unruh and Gibbons-Hawking. We also derive the exact evolution operator and master equation for the reduced density matrix of the system interacting with a parametric oscillator bath in an initial squeezed thermal state. These results are useful for decoherence and backreaction studies for systems and processes of interest in semiclassical cosmology and gravity. Our model and results are also expected to be useful for related problems in quantum optics. %\pacs {05.40.+j,03.65.Sq,98.80.Cq,97.60.Lf}Comment: 42 pages, Latex, umdpp93-210 (submitted to Physical Review D, 3 December 1993