Towards a systematic understanding of the post-inflationary reheating history in interacting scalar field models

The present thesis is devoted to the investigation of the post-inflationary reheating phase. This phase represents the transition of the Universe from the end of inflation into its radiation dominated state before the onset of Big Bang Nucleosynthesis. Characterising this stage is relevant for two reasons. First, any inflationary model can only work properly, when the energy transfer from the inflationary sector to eventually the constituents of the Standard Model of particle physics is ensured. And second, accurate predictions of the CMB observables require a complete understanding of the expansion history of the Universe, that includes in particular the reheating phase.
In the main body of this work we investigate this phase in the context of inflaton potentials that have monomial shape around their minimum and possibly a non-zero vacuum expectation value. For the preheating sector we consider a very general class of reheating models, where the inflaton field may couple to other, single or multiple, interacting scalar fields (referred to as daughter fields). These interactions in the preheating sector comprise quadratic-quadratic and emergent trilinear interactions (in case of a non-zero vacuum expectation value) between inflaton and scalar fields, quartic self-interactions of single daughter fields, as well as quadratic-quadratic interactions between different daughter fields.
In our endeavour to provide a comprehensive understanding of this post-inflationary phase, we first investigate by analytic and semi-analytic measures, in the context of a linearised theory, the resonance effects that emerge during the early stage of preheating. We then turn to classical lattice simulations, by which we characterise the whole preheating phase from the end of inflation until the system arrives at a stationary regime. In this study we focus on two major aspect, the evolution of the energy distributions of the different fields and the equation of state. Finally, by knowing the evolution of the equation of state we will be able to determine the full expansion history of the Universe from the end of inflation until the present, which will allow us to give significantly improved predictions for the CMB observables.