Does de Sitter space belong to the Swampland?

 String theory is a theory of gravity and matter interactions that is UV complete (it is valid at high energies). It is moreover known for its formal applications and breakthroughs. The real question, i.e. how it relates to physics at accessible energy scales, still remains a worry and is often debated in the field. Very recently research on that front has seen a paradigm shift and researchers are realising that string theory predicts very sharp bounds on the space of possible low energy theories. This gives significantly more hope that the theory can be falsified. Hence the study of these bounds became an important goal in the field. One conjectured bound, which lacks clear evidence, is one on the equation of state parameter of dark energy. It is conjectured by some leading researchers in the field that it should be greater than minus one, implying that dark energy is decaying slowly. This could be measurable in the near future. My project consists in either finding more evidence for this important conjecture or evidence against it. I plan to investigate this both from the point of view of ten-dimensional string theory as from four-dimensional quantum field theory in curved spacetime.