Numerical Quantum Field Theory on the Continuum and a New Look at Perturbation Theory

The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral representations of the Green's functions by Sinc function expansions are an extremely powerful calculative tool. Specifically, this understanding makes it not only possible to apply the Source Galerkin method to higher dimensional field theories, but also leads to a new approach to perturbation theory calculations in scalar and fermionic field theories. This report summarizes the methodologies for solving quantum field theories with the Source Galerkin method and for performing perturbation theory calculations using Sinc approximations.Comment: Lattice2001(theorydevelop

Generating Gravitational Waves After Inflation

I review two mechanisms by which gravitational waves can be generated at the end of inflation: preheating, and gravitons Hawking radiated during the decay of very small primordial black holes. These mechanisms are contrasted with the gravitational waves during inflation, and may provide a window into the physical processes that govern the end of the inflationary phase.Comment: Conference proceeding

Inhomogeneity and Nonlinear Preheating

We investigated the possibility that nonlinear gravitational effects influence the preheating era after inflation, using numerical solutions of the inhomogeneous Einstein field equations. We compared our results to perturbative calculations and to solutions of the nonlinear field equations in a rigid (unperturbed) spacetime, in order to isolate gravitational phenomena. We confirm the broad picture of preheating obtained from the nonlinear field equations in a rigid background, but find gravitational effects have a measurable impact on the dynamics. The longest modes in the simulation grow much more rapidly in the relativistic calculation than with a rigid background. We used the Weyl tensor to quantify the departure from homogeneity in the universe. We saw no evidence for the sort of gravitational collapse that leads to the formation of primordial black holes.Comment: Talk given at Marcel Grossmann Meeting IX. 3 pages, 1 figur