Quantum Gravity and Entanglement

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Entanglement, the unique property of quantum mechanics that prevents the description of a system by just looking at the properties of its individual components, is a centerpiece in current research in diverse areas of physics spanning from quantum information science to condensed matter physics to quantum field theory. The main objective of this research is to understand the role of entanglement in the description of the quantum nature of space-time. This works investigates fundamental puzzles in theoretical physics such as the description of the primordial state of the universe and the fate of information in black hole evaporation. The focus is on universal aspects of space-time entanglement that can provide valuable insights for any theory of quantum gravity. At the Planck scale new quantum effects that go beyond Einstein's general relativity are expected to dominate. Loop quantum gravity is one of the leading candidate theories for describing the physics in these regimes. In this theory, space-time has a granular structure that arises as a foam-like excitation of a topologically invariant vacuum. From this perspective, space-time is made of 'elementary constituents' and, as in condensed matter physics, it can have different quantum phases. The main open problem is to identify the quantum phase that describes our smooth extended space-time. A set of techniques that were recently developed in condensed matter physics will be used to study the amount of entanglement between quantum geometry degrees of freedom. This research will directly address the question of the quantum nature of space-time. The results of this research on entangled-network states will provide the basis for extracting physical properties of space-time states in quantum gravity. Three directions will be investigated. The first regards the Minkowski space-time state where the entangled-network state is obtained via a variational ansatz for the minimization of the ADM energy. The second direction regards the use of entangled-network states in quantum cosmology, the study of entanglement near classical singularities, and the thermalization time of subsystems in the de Sitter expansion phase. The third direction regards black hole space-times, the relation between entanglement entropy and black hole entropy, and the dynamics of entanglement entropy in the evaporation process.