Gravity beyond General Relativity in anti-de Sitter and de Sitter spacetimes

More than a century after its formulation, General Relativity still passes every single experimental and observational test that physicists have designed. However, this does not mean that it is a complete theory of gravity, but rather that observations are not accurate enough to falsify it yet. In this thesis, several theoretical extensions of General Relativity are considered and some of their implications are investigated. Important developments in the past decades have demonstrated that General Relativity considered in anti-de Sitter spacetimes (AdS) can be used to study strongly interacting conformal field theories (CFT). We use this fruitful AdS/CFT connection to study out-of-equilibrium quantum dynamics, and we develop an understanding of thermalization and quantum chaos in terms of gravitational black hole physics. This description allows us to characterize these quantum phenomena in regimes where conventional computational methods fail. In gravitational language, thermalization corresponds to the disappearance of matter behind a black hole’s event horizon, to which one can associate thermal properties such as temperature and entropy. On the other hand, chaos emerges from the gravitational blueshift of particles falling into a black hole, causing them to interact strongly with other particles traveling near the black hole horizon. In parallel, we study vacuum quantum fluctuations in cosmology, considered one of the best observational windows into fundamental physics. A potentially major role of quantum fluctuations is their contribution to the cosmological constant, which sources the accelerated expansion of our Universe. We revisit the tension between theory estimates and cosmological measurements of the cosmological constant and propose a low-energy effective theory that might potentially resolve this tension. In this model, the cosmological dynamics of a new scalar field tends to screen most of the vacuum energy, such that the Hubble expansion rate is relaxed to the observed small value. Lastly, we also contribute to the development of the AdS/CFT correspondence in application to cosmology, which enables us to generalize part of the known vacuum structure of free quantum fields in de Sitter space. In particular, we find that analogues of the Mottola-Allen vacua also appear in the context of AdS/CFT.