In this thesis a systematic approach is taken to the study of the generation of primordial perturbations from a nite amount of cosmic in ation. It is demonstrated how a pre-in ationary stage that is kinetically dominated causes features in the primordial power spectrum. These features can be associated with cosmological parameters, which are then constrained using Bayesian methods and CMB data from the Planck satellite.

Chapter 1 places this thesis into the context of the current state of cosmology and introduces the needed theoretical background and notation. The remainder of the thesis presents both my published and ongoing work.

Chapter 2 starts with an overview of Bayesian methods which are then applied to the question of how a uniform versus logarithmic prior distribution a ect parameter estimations and model comparisons. Two examples of extensions to the current standard model of cosmology are investigated in detail, the tensor-to-scalar ratio of primordial perturbations and three massive neutrinos.

Chapter 3 was published in Hergt et al. (2019) [I & chapter 3] and makes a case for a pre-in ationary phase of kinetic dominance. To that end the phase-space trajectories for three representative in ationary potentials are inspected. Comparing di erent priors on the initial conditions of the trajectories, a signi cant fraction of trajectories are found to start out in a kinetically dominated stage.

Chapter 4 was published in Hergt et al. (2019) [II & chapter 4]. Assuming a spatially at cosmology, it contrasts the e ects from slow-roll in ation to those from a nite amount of in ation with an earlier kinetically dominated stage. CMB data from the Planck satellite are used to compare these two models and constrain the parameters pertaining to the primordial Universe. There is no clear preference for either model. Any Occam penalty from the higher complexity of a model with a kinetically dominated stage is balanced out by a better t to the large-scale lack of power in the CMB.

Chapter 5 extends the previous analysis, allowing for a variable amount of spatial curvature. Even a small amount of present-day curvature signi cantly limits the total amount of in ation, rendering the e ects of kinetic dominance more prominent in the observable window of the CMB. A model comparison of various single- eld in ation models leads to similar results to those of a at cosmology, driven mostly by constraints from the tensor-to-scalar ratio and from reheating.

I conclude with potential directions of future research.