Moduli stabilisation and soft supersymmetry breaking in string compactifications

In this thesis, we shall work in the framework of type IIB Calabi-Yau flux compactifications and present a detailed review of moduli stabilisation studying in particular the phenomenological implications of the LARGE-volume scenario (LVS). All the physical relevant quantities such as moduli masses and soft-terms, are computed and compared to the phenomenological constraints that today guide the research. The structure of this thesis is the following. The first chapter introduces the reader to the fundamental concepts that are essentially supersymmetry-breaking, supergravity and string moduli, which represent the basic framework of our discussion. In the second chapter we focus our attention on the subject of moduli stabilisation. Starting from the structure of the supergravity scalar potential, we point out the main features of moduli dynamics, we analyse the KKLT and LARGE-volume scenario and we compute moduli masses and couplings to photons which play an important role in the early-universe evolution since they are strictly related to the decay rate of moduli particles. The third chapter is then dedicated to the calculation of soft-terms, which arise dynamically from gravitational interactions when moduli acquire a non-zero vacuum expectation value (VeV). In the last chapter, finally, we summarize and discuss our results, underling their phenomenological aspects. Moreover, in the last section we analyse the implications of the outcomes for standard cosmology, with particular interest in the cosmological moduli problem.