Hal Finkel

Well-known problems with standard big-bang cosmology motivate the inflationary scenario. A large class of inflationary models can be described using the slow-roll formalism, in which a set of interacting, classical scalar fields drive the expansion of the very early universe. In order to explain how inflation ends while quickly reheating the universe, many slow-roll models are constructed to contain a parametric-resonance-driven preheating phase. This phase is driven by non-perturbative processes, and fully understanding its properties requires the use of 3-D numerical simulations. This dissertation discusses PSPECTRE, a pseudo-spectral code for simulating post-inflationary preheating. Compared to existing codes, PSPECTRE displays excellent convergence and can often obtain reliable results using a substantially-smaller number of grid points. A generic class of preheating models have been predicted to generate a copious quantity of oscillons. Oscillons are long-lived, oscillatory, spatially-localized solutions to nonlinear scalar-field models. Using PS PECTRE, oscillon-generating preheating models have been investigated, and it has been confirmed that a large class of these models predict a post-preheating oscillon-dominated phase. In such an oscillon-dominated phase, the universe evolves as would a traditional matter-dominated universe, and this significantly alters how these models must be evaluated. Initial applications of PS PECTRE to investigating gravitational-wave observables are also discussed.