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Towards String Theory models of DeSitter Space and early Universe Cosmology

String theory is arguably the best candidate for a theory of quantum gravity and unified interactions. Reconciling Einstein's theory of General Relativity with Quantum Mechanics. The theory however is best understood on Minkowski and Anti-de Sitter space-times, and not on exponentially expanding space-times with positive cosmological constant, like our own universe. There is still no satisfactory formulation of String Theory on these so called asymptotically de Sitter space times. In this thesis I will discuss certain avenues of progress towards a String Theory formulation of de Sitter space-times. Specifically, how understanding of the analytic continuations of Liouville Theory and how to gauge-fix it in the Timelike regime will aid in the understanding of the proposed FRW-CFT duality of de Sitter space. It is also discussed how non-trivial topology effects proposed Chern-Simons Matter duals of Vasiliev Higher Spin gravity theories which are important in the dS-CFT description of de Sitter Space.