In this thesis, we discuss several instances in which non-linear behaviour affects cosmological evolution in the early Universe. We begin by reviewing the standard cosmological model and the tools used to understand it theoretically and to compute its observational consequences. This includes a detailed exposition of cosmological perturbation theory and the theory of inflation. We then describe the results in this thesis, starting with the non-linear evolution of the curvature perturbation in the presence of vector and tensor fluctuations, in which we identify the version of that variable that is conserved in the most general situation. Next, we use second order perturbation theory to describe the most general initial conditions for the evolution of scalar perturbations at second order in the standard cosmological model. We compute approximate solutions valid in the initial stages of the evolution, which can be used to initialize second order Boltzmann codes, and to compute many observables taking isocurvature modes into account. We then move on to the study of the inflationary Universe. We start by analysing a new way to compute the consequences of a sudden transition in the evolution of a scalar during inflation. We use the formalism of quantum quenches to compute the effect of those transitions on the spectral index of perturbations. Finally, we detail the results of the exploration of a multi-field model of inflation with a non-minimal coupling to gravity. We study popular attractor models in this regime in both the metric and the Palatini formulations of gravity and find all results for both the power spectrum and bispectrum of fluctuations to closely resemble those of the single-field case. In all systems under study we discuss the effects of non-linear dynamics and their importance for the resolution of problems in cosmology.
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