Fuzzy dark matter from string axions

In this thesis we study the viability for ultra-light axions coming from moduli stabilisation in the Large volume scenario to fit recent observations about the dark matter presence in several galaxies and clusters. After a historical introduction on the dark matter problem and a review of the candidates proposed as dark matter constituents through the years, in Chapter 1 we present WIMPs and ALPs, which are nowadays believed to be the most likely constituents. In Chapter 2 we give the theoretical basis to analyse these particles, that is Supersymmetry and String theory, focusing especially on dimensional reduction and string compactifications in order to derive an effective theory. Then, in Chapter 3 we discuss the issue of moduli stabilisation and we deal with it in the Large volume scenario, examining the examples of Swiss cheese and Fibred Calabi-Yau manifolds. Finally, in Chapter 4 we present the original results of this thesis. Starting from recent observations claiming the existence of a preferred range of masses for the ultra-light axions constituting dark matter, we provide a theoretical explanation in the Large volume scenario. We demonstrate that a preferable mass exists for these axions and that axions having this mass could account for the total observed dark matter abundance in a natural way. In addition to this, we examine how to provide several axions with different masses by imposing reasonable cosmological hierarchies. Finally, we show how to generalise these results to Calabi-Yau manifolds with any number of axions, while in Chapter 5 some interesting outlooks of the present work are discussed.