Holographic Cosmological Models and the AdS/CFT Correspondence

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The formulation of a quantum theory of gravity is a central open problem in theoretical physics. In recent years, the development of holography---and in particular the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence---provided a new framework to investigate quantum gravity and led to consistent advancement. However, how to describe cosmology within holography remains an unanswered question whose solution could determine whether holography is able to capture physics in our universe.

This dissertation describes a new proposal for embedding cosmological physics in the holographic paradigm. This is articulated in two different but related approaches, both involving time-symmetric Big Bang-Big Crunch cosmologies with negative cosmological constant $\Lambda$.In the first approach, the cosmological universe is given by a four-dimensional end-of-the-world brane moving in a five-dimensional AdS black hole spacetime. The proposed holographic dual description is given by a boundary conformal field theory. Under specific conditions, gravity is localized on the brane and effectively four-dimensional: an observer living on the brane is unaware of the existence of the extra dimension. In this dissertation, I show how these conditions can be met in an AdS-Reissner-Nordstr"om background while retaining a holographic dual description.

The second approach focuses on spatially flat $\Lambda<0$ cosmologies which analytically continue to Euclidean wormholes connecting two asymptotic AdS boundaries. The proposed dual theory is given by two holographic 3D CFTs coupled by non-holographic 4D degrees of freedom on a strip. A different analytic continuation of the Euclidean wormhole leads to a Lorentzian traversable wormhole. After discussing the general features of these holographic cosmologies, I describe how the traversable wormhole can be reconstructed from the dual theory and how the existence of the former constrains the latter. Finally, I show that these $\Lambda<0$ cosmologies can undergo phases of accelerated expansion and match observational data for the scale factor evolution.

The results presented in this dissertation should be regarded as the initial steps on a new line of research which will hopefully lead to a description of quantum gravity in a cosmological universe via holography. Achieving this goal would render holography a viable candidate to describe quantum gravity in our universe.