Probes of the cosmic microwave background have revealed a spatially flat and highly isotropic early Universe, seeded with small gaussian primordial perturbations characterized by a nearly scale-invariant power spectrum. The physics responsible for sourcing this early state, how-ever, is still a subject of debate and remains largely speculative. This work explores the-oretical and computational methods with the aim of further understanding the physical mechanisms which were at play during this early phase of our Universe.

An early period of accelerated cosmic expansion, known as inflation, is one possible sce-nario which has been proposed to account for the above-mentioned large-scale properties of our Universe. It is therefore of interest to place observational constraints on inflationary dynamics in order to better understand its physical origin. To that end, in the first original portion of this work, we employ quantum mechanical inverse-scattering techniques with the aim of shedding light on the stress-energy responsible for this proposed early inflationary state. In particular, we demonstrate a numerical reconstruction of two simulated inflation-ary histories assuming perfect knowledge of their corresponding observables. Taking stock of these results, we then briefly discuss the application of this technique to more realistic cases incorporating uncertainties and limited access to cosmological data.

Subsequently, in the second original portion of this thesis, we investigate the effects of quantum particle production on the cosmic evolution. This effect is particularly relevant for models of the very early Universe, when the energy density generated through this process may back-react on the cosmological expansion. Here we demonstrate a numerical solution to the back-reaction problem in regimes dominated by particle production. Finally, we discuss the relevance of quantum particle production to bounce and inflationary models of the early Universe.