Time-dependent Backgrounds in String Theory and Dualities

This thesis consists of two parts. The first part deals with gauge/gravity duality in the context of anti de Sitter (AdS) spacetimes with de Sitter (dS) boundary, which can be used to study issues concerning strongly coupled field theory on de Sitter space, such as the issue of vacuum ambiguity. By calculating the symmetric two point function of the strongly coupled ${\cal N} = 4$ supersymmetric Yang-Mills theory on de Sitter space, we show that the vacuum ambiguity persists at strong coupling. Furthermore, the extra ambiguity in the strong coupling correlator seems to suggest that transition between two different vacua is allowed. The second part of this thesis deals with the duality between the rolling tachyon backgrounds in superstring theory and the Dyson gas systems. This duality can be interpreted as a reformulation of non-BPS D-branes in superstring theory in terms of statistical systems in thermal equilibrium, whose description does not include time. We argue that even though the concept of time is absent in the statistical dual sitting at equilibrium, the notion of time can emerge at the large number of particles $N \rightarrow \infty$ limit