| Summary: | This thesis focuses on applying worldsheet conformal field theories to study problems of time-dependence and moduli stabilisation as motivated by string cosmology. Firstly, we construct exact string backgrounds using conformal field theories where the compact sectors are chosen such that the massless scalar moduli are naturally frozen. We term these models 'Gepner models' as they are related to the usual algebraic compactifications called Gepner models. The sign of the charge deficit categorises the compactifications into two branches, one of whom requires D-branes to stabilise the dilaton potential, resulting in a small negative cosmological constant. Secondly, we discuss tools to study the timelike Liouville theory for the supersymmetric case. We attempt to define the timelike supersymmetric Liouville theory for the N = 1 case via an analytic continuation of the shift relations of the spacelike theory. Our methods have not yet led to a diagonal two-point function for the timelike N = 1 theory.
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