In this thesis we analyze a very simple model of two dimensional quantum gravity based on causal dynamical triangulations (CDT). We present an exactly solvable model which indicates that it is possible to incorporate spatial topology changes in the nonperturbative path integral. It is shown that if the change in spatial topology is accompanied by a coupling constant it is possible to evaluate the path integral to all orders in the coupling and that the result can be viewed as a hybrid between causal and Euclidian dynamical triangulation. The second model we describe shows how a classical geometry with constant negative curvature emerges naturally from a path integral over noncompact manifolds. No initial singularity is present, hence the quantum geometry is naturally compatible with the Hartle Hawking boundary condition. Furthermore, we demonstrate that under certain conditions the quantum fluctuations are small! To conclude, we treat the problem of spacetime topology change. Although we are not able to completely solve the path integral over all manifolds with arbitrary topology, we do obtain results that indicate that such a path integral might be consistent, provided suitable causality restrictions are imposed.
To a significant extent, the metrical and topological properties of spacetime can be described purely order-theoretically. The $K^+$ relation has proven to be useful for this purpose, and one could wonder whether it could serve as the primary causal order from which everything else would follow. In that direction, we prove, by defining a suitable order-theoretic boundary of $K^+(p)$, that in a $K$-causal spacetime, the manifold-topology can be recovered from $K^+$. We also state a conjecture on how the chronological relation $I^+$ could be defined directly in terms of $K^+$.
We introduce a framework to study the emergence of time and causal structure in quantum many-body systems. In doing so, we consider quantum states which encode spacetime dynamics, and develop information theoretic tools to extract the causal relationships between putative spacetime subsystems. Our analysis reveals a quantum generalization of the thermodynamic arrow of time and begins to explore the roles of entanglement, scrambling and quantum error correction in the emergence of spacetime. For instance, exotic causal relationships can arise due to dynamically induced quantum error correction …
Emergence of Dark Energy from topology and chiral spinors
Universidad de La Frontera（弗雷罗纳大学）；Universidad de La Serena（拉塞雷纳大学）；Lanzhou University（兰州大学）；Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa（里斯本大学空间天体物理研究所）；Université de Paris-Cité（巴黎西岱大学）
Four-dimensional CDT (causal dynamical triangulations) is a lattice theory of geometries which one might use in an attempt to define quantum gravity non-perturbatively, following the standard procedures of lattice field theory. Being a theory of geometries, the phase transitions which in usual lattice field theories are used to define the continuum limit of the lattice theory will in the CDT case be transitions between different types of geometries. This picture is interwoven with the topology of space which is kept fixed in the lattice theory, the reason being that "classical" geometries arou…
We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with many outgrowths, which contain most of the four-volume and which have almost spherical topologies, but nevertheless are quite fractal.
