The entangled universe

In this doctoral thesis we discuss topics in holography and cosmology. In the first part of the thesis, we introduce the concept of holography, which relates models with gravity to models without gravity in one dimension less. We describe some techniques in holographic reconstruction and point out that there are limitations to these techniques. In particular, certain regions in the gravitational model cannot be probed with existing techniques and we refer to these regions as holographic shadows.
Subsequently, we discuss a proposed holographic probe called causal holographic information. We investigate some properties and discuss possible interpretations of causal holographic information in the non-gravitational model. We point out that causal holographic information has a particular divergence structure, which can be written in terms of nonlocal quantities.
In the second part of the thesis we discuss two topics in cosmology. Firstly, we analyze a class of non-minimally coupled single field inflation models in two different limits: the strong non-minimal coupling limit and the weak non-minimal coupling limit. These limits correspond to special models, called attractor models.
Subsequently we discuss the topic of cosmology in a hyperbolic section of de Sitter spacetime. The hyperbolic patch can be seen as a toy model for a bubble universe. We investigate two different quantum states: the natural hyperbolic vacuum and the Bunch Davies state. We conclude that their different imprints on the cosmic microwave background hard to distinguish at observable scales.