Physics aims to describe nature on all scales and as such its holy grail is to find a theory of quantum gravity. Currently, the best candidate for the theory of quantum gravity is string theory. If string theory is the correct theory of nature, we need to be able to build a model of the universe within this theory which is consistent with current observations and that can make predictions for upcoming observations. In this thesis we focus on specific properties of cosmological model building in string theory and on the wave function approach to the de Sitter/Conformal Field Theory correspondence (dS/CFT), which taken together allow us to make observational predictions in string theory. In the first part of the thesis we focus on the fact that in string theory compactifications one often simplifies the full ten-dimensional theory by smearing the sources over the internal manifold, which corresponds to an effective lower dimensional gauged supergravity. This smeared limit is identical to the approximation that ignores warping. It is therefore relevant to compare quantities obtained from the effective gauged supergravity with the true ten-dimensional solution with localised sources. We calculate the correspondence between BPS (Bogomol'nyi–Prasad–Sommerfield) domain walls in gauged supergravity and ten-dimensional supergravity with localised sources. We find that the domain wall energy is unaffected by the localisation of the sources. Then we focus on a specific way to realize the de Sitter uplift in the KKLT (Kachru-Kallosh-Linde-Trivedi) scenario using nilpotent chiral superfields. This type of field allows for de Sitter vacua in supergravity, without any additional scalars, making them ideal candidates for cosmological model building. We review the properties and status of nilpotent chiral superfields and explain how they can be used to build de Sitter vacua. We also construct the general supergravity action for a nilpotent chiral superfield, coupled to an arbitrary number of chiral and vector multiplets. In the second part of this thesis we first explain how the cosmological saddle points of the no-boundary wave function can have a Euclidean anti-de Sitter (AdS) representation and we will explore its properties. This makes it possible to study the prediction of the wave function for the primordial power spectrum, when turning on a single scalar field, from an AdS perspective. The complexity of the AdS domain wall has an effect on the quantum state of the fluctuations and thus on the prediction for the primordial power spectrum. We explicitly calculate this effect and contrast our results with dS/CFT proposals that rely on a procedure of analytic continuation to AdS. We find that both proposals agree to leading order in the slow roll parameters, but they differ at higher order. Finally we propose a holographic formulation of the tunneling wave function. We show that the no-boundary wave function corresponds to a decaying wave function in the AdS representation, while the growing wave function, familiar from other applications of Euclidean AdS/CFT, corresponds to the tunnelling wave function. As a first test of the proposal for a holographic tunneling state we compute the partition function of the O(N) vector model and show that it qualitatively agrees with the wave function results.