Magíster en Ciencias, Mención Física / The standard model of cosmology has some problems in order to describe the early stages of the universe. The theory of Cosmic Inflation, a phase of accelerated exponential expansion, was conceived to solve the previous problems in the model and it ended up giving an explanation for the primordial seeds of the universe. In this thesis, which consists of two parts, we study the effect of extra degrees of freedom during the inflationary era and their implications for the primordial statistics of the universe. In the first part, we study the creation of \textit{features} in the primordial scalar power spectrum resulting from temporary deviations from a quasi de-Sitter background. Specifically, how we can correlate scalar features to the ones in the primordial tensor power spectrum. We notice that these deviations from scale invariance are related via slow roll parameters. We derive a general relation linking features in the spectrum of curvature perturbations to the features in the spectrum for the tensor perturbations. We conclude that, even with large deviations from scale invariance in the curvature power spectrum, the tensor power spectrum remains scale invariant for all observational purposes. The second part is about the analysis of the inflationary landscape characterized by a multi-scalar field potential with many local minima. If this is the case, the quantum fluctuations of the scalar field had a chance to experience excursions traversing many local minima of the landscape potential. We study this situation by analyzing the dynamics of an axion-like field $\psi$ present during inflation, with a potential given by $v(\psi) = \Lambda^4 (1 - \cos (\psi / f))$. By assuming that the vacuum expectation value of the field is stabilized at one of its minima, say $\psi = 0$, we compute every $n$-point correlation function of $\psi$ to first order in $\Lambda^4$ using the \emph{in-in} formalism. This computation, which requires a resummation of all the loops due to the non-linear nature of $v(\psi)$, allows us to find the distribution function describing the probability of measuring $\psi$ at a particular field-value during inflation. Because $\psi$ is able to tunnel between the barriers of the potential, we find that the probability distribution function consists of a non-Gaussian multi-modal distribution such that the probability of finding $\psi$ near a given minimum of $v(\psi)$, different from $\psi=0$, increases with time. / Este trabajo ha sido parcialmente financiado por Proyecto Fondecyt 1171811