Non-linear scalar field dynamics in particle physics motivated models of the early universe

In particle physics motivated models of the early universe, non-linear preheating dynamics of scalar fields can give rise to rich phenomenology. An example phenomenon is e.g. the formation of oscillons:
quasi-stable, localised, and non-linear scalar field configurations. In the first of three main parts of this thesis we study the gravitational wave (GW) production of asymmetric (ellipsoidal) oscillons in an expanding universe. Based on model-independent, simplifying assumptions on the properties of oscillons, we derive an analytical expression for the anisotropic stress tensor. The latter is subsequently used to numerically compute the stochastic GW background of different "oscillon cosmologies". In particular, we investigate and discuss how different properties of an oscillon cosmology, such as the background expansion or the size, and amplitude of oscillons, manifest themselves in the stochastic background of GWs.

The second and third part of this thesis are devoted to lattice studies in which the non-linear scalar field dynamics, as well as the associated production of GWs is explored in different models.
In the second part we consider different realisations of a supersymmetric model of hilltop inflation in which an additional scalar field $\chi$ couples to the inflaton. We find that during preheating $\chi$ can get resonantly amplified due to a non-standard parametric resonance that is driven by the dynamics of inhomogeneous inflaton fluctuations. Moreover, we show that qualitative differences in the dynamics of the fields are manifested in the resulting GW background.

In the third part we consider the non-linear dynamics of Kähler moduli in two scenarios of moduli stabilisation in type IIB string theory. More explicitly we study the dynamics of the overall volume modulus in the Kachru-Kallosh-Linde-Trivedi (KKLT) scenario, as well as the dynamics of a single blow-up modulus in the Large Volume Scenario (LVS). More specifically, we consider the dynamics of preheating of moduli that get displaced from their post-inflationary minimum through the "vacuum misalignment" mechanism. In both models we show that preheating can be very efficient and lead to the non-linear fragmentation of the moduli and, ultimately, to the formation of oscillons. Interestingly, we find that the dynamics are qualitatively different in the KKLT scenario compared to the dynamics of the blow-up modulus in the LVS. The corresponding differences are also imprinted in the resulting GW background.