Initial conditions for axion hilltop quintessence in string theory

The main objective of this thesis is to investigate a mechanism to dynamically set the initial conditions of an axion hilltop quintessence model embedded in the framework of Type IIB String Theory. In order to account for the phenomenology of a Dark Energy-driven expansion, the quintessence axion must sit near the hilltop, particularly when its decay constant is sub-Planckian, as in the case where the effective field theory is under control. Our approach aims to reduce the need for extreme fine-tuning by exploiting moduli stabilisation rather than relying on arbitrarily chosen initial conditions. The dynamical mechanism is based on the fact that in the early Universe the potential of the quintessence axion features a minimum in the place where it develops a maximum in the late Universe. The quintessence potential changes its shape thanks to the evolution of an open string field which controls the strength of non-perturbative contributions. The effective 4-dimensional theory arises from the compactification of the 10-dimensional theory on a K3-fibred Calabi-Yau manifold, within the Large Volume Scenario. The quintessence field is identified with an ultra-light K\"{a}hler axion, whose potential is generated non-perturbatively, and doubly exponentially suppressed by poly-instanton effects. We examine two mechanisms that can naturally lead to the required initial conditions, both relying on closed-open string interactions in the presence of D-branes. The first scenario includes de-sequestering effects from open string contributions in the presence of D3-branes at an orbifold singularity. The second one introduces instead shift-symmetric open string moduli on D7-branes, which couple to geometric moduli and allow for a controlled evolution towards the quintessence regime. For each scenario, we analyse the scalar potential, the mass hierarchies and the field dynamics during and after inflation.