Instabilities of string vacua and cosmological spacetimes

Recent studies of gravitational low-energy effective theories have revealed that high-energy quantum gravity effects do not always decouple at low energies. This suggests that quantum gravity might have universal low-energy predictions. In this thesis, we study quantum gravity in the context of extremal black holes, anti-de Sitter space and de Sitter space. In particular, we investigate the consequences of these effects on low-energy effective theories. We find that quantum effects allow nonsupersymmetric extremal black holes to decay by emitting a charged state when the Weak Gravity Conjecture is satisfied. This implies that the near-horizon anti-de Sitter space can also decay with a probability that is set by the Bekenstein-Hawking entropy of the extremal black hole. Next, we focus our attention on de Sitter space and argue that the quantum state that describes the expansion of our universe is given by a previously unexplored state: the Unruh-de Sitter state. We explicitly construct this state and show that it breaks some of the de Sitter isometries. As a result, backreaction effects put a fundamental bound on the lifetime of an expanding universe in the Unruh-de Sitter state given by the Gibbons-Hawking entropy. Finally, we study supersymmetry breaking in de Sitter space in the context of string theory. We show that in the KKLT scenario anti-D3-branes break supersymmetry spontaneously, which supports the claim that this construction gives rise to metastable de Sitter vacua.