Quantum gravity and Cosmological models on finite space-times
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We study different quantum geometries using the Quantum Riemannian Geometry (QRG) formalism, constructing some quantum gravity and cosmological models over them. First, we fully solve the quantum geometry of Zn as a polygon graph for a moduli of metrics with square-lengths on the edges. The classical limit for n → ∞ is analysed and, corre- lation functions are numerically calculated for Euclidean quantum gravity for 3 ≤ n ≤ 6. An FLRW model is analysed adding ‘classical’ time, finding the same expansion rate as for the classical flat FLRW model in 1+2 dimensions, i.e. a dimension jump. We ap- ply the adiabatic particle creation method on R × Zn. Also, a Schwarzschild black hole model is proposed with classical time and radius where the Laplacian and the classical limit Zn → S 1 are studied. Using the quantum geometry of a fuzzy sphere as a base space, it is constructed an FLRW and a spherically-symmetric black hole adding classical coordinates of time and radius as appropriate. The Schwarzschild black hole model with static-spherical solutions for Ricci = 0 is developed. A dimension jump is also found in this model with solutions having the time and radial form of a classical 5D Tangherlini black hole. Finally, we solve for quantum Riemannian geometries on the finite lattice interval • − • − · · · − • with n nodes (the Dynkin graph of type An) and find that they are necessarily n+1 q-deformed with q = e ıπ . Specifically, we discover a novel ‘boundary effect’ whereby, in order to admit a quantum-Levi Civita connection, the ‘metric weight’ at any edge is forced to be greater when pointing towards the bulk compared to towards the boundary. The Laplacian and QFT are studied under this geometry as quantum gravity for n = 3. Although, the models are constructed using different geometries, the techniques used for constructing and solving them are analogous and show some similarities which ap- parently are always present. It is needed to construct more examples to identify which similarities are general.
Authors
Argota Quiroz, JNCollections
- Theses [4190]