Obstacles to realizing Quintessence from String Theory

In this master thesis we analyze the construction of quintessence models by flux compactification of type IIB string theory. We focus on Kähler moduli as candidates for the quintessence field and briefly comment on other approaches. The large hierarchies required for simultaneously describing quintessence and the standard model pose a major challenge to model building and depend upon parametric control over the scalar potential, which is gained in the limit of large compactification volume. Further suppression of the quintessence scale can be achieved by an anisotropic compactification. However, by lowering the quintessence mass we also lower the masses of several other fields. As has been noticed before, the volume modulus becomes too light to avoid fifth-force constraints. We call this the "light volume problem". Furthermore, the masses of the SUSY partners of standard-model fields turn out too light as well, so we need a further source of SUSY breaking. Introducing an appropriate SUSY-breaking hidden sector on the standard-model brane then leads to a large positive F-term contribution to the scalar potential that cannot be canceled by the known negative terms and thus significantly raises the vacuum energy. To cancel the F-term, it would take an equally large negative contribution, which is currently unknown. In the context of the de Sitter swampland conjecture, this "F-term problem" raises yet another question. If we manage to cancel the F-term with some large additional contribution, a tiny change of parameters in the SUSY-breaking sector could de-tune this cancellation and uplift the potential to de Sitter. Since the conjecture does not allow for such potentials, there has to be some mechanism preventing the uplift