For more than 80 years theoretical physicists have been trying to develop a theory of quantum gravity which would successfully combine the tenets of Einstein’s theory of general relativity (GR) together with those of quantum field theory. At the current stage, there are various competing responses to this challenge under construction. Attacking the problem of quantum gravity from the quantum geometry perspective, where space and spacetime are discrete, the focus of this thesis lies on the application of loop quantum gravity (LQG) and group field theory (GFT). We employ these two closely related non-perturbative approaches to two areas where quantum gravity effects are broadly expected to be relevant: black holes and quantum cosmology.
Concerning black holes, apart from understanding their inner structure, the most pressing issue is to give a microscopic explanation for the phenomenon of black hole entropy in terms of a discrete quantum geometry and relate it to the symmetries of the horizon. Black hole models in LQG are typically constructed via the isolated horizon boundary condition which gives rise to an effective description of the horizon geometry in terms SU(2) Chern-Simons theory. The quantum statistical analysis of this configuration allows to retrieve its entropy which is compatible with the semi-classical Bekenstein-Hawking area law. In this thesis we find a reinterpretation of the statistics of the horizon degrees of freedom as those of a system of non-Abelian anyons.
As regards quantum cosmology, the challenge is to understand how the initial singularity problem of GR can be resolved by means of the discreteness of geometry and how a spacetime continuum can emerge from a large assembly of geometric building blocks. Most recent research in GFT and its condensate cosmology spin-o˙ aims at deriving the effective dynamics for GFT condensate states directly from the microscopic GFT quantum dynamics and subsequently to extract a cosmological interpretation from them. The central conjecture of the condensate cosmology approach is that a possible continuum geometric phase of a particular GFT model is ideally approximated by a condensate state which is considered suitable to describe spatially homogeneous universes. By exploring this idea, new perspectives are revealed for addressing the long-standing question of how to recover the continuum from the collective behaviour of a large set of geometric building blocks in LQG. Remarkably, these efforts have shown that quite naturally a bouncing cosmological solution can be obtained. Its dynamics at late times can be cast into the form of effective Friedmann equations for an isotropic and homogeneous universe.
In this thesis we elaborate on aspects of the above-mentioned conjecture of the condensate phase and study phenomenological consequences of this approach in detail. In particular, we find condensate configurations consisting of many smallest building blocks which may give rise to an effectively continuous emergent geometry in various models. We also explore the cosmological implications of effective interactions between the quantum geometric constituents of the condensate for the first time and show how such interactions can lead to a recollapse or infinite expansion of the emergent universe while preserving the bounce and demonstrate that fine-tuned interactions can lead to an early epoch of accelerated expansion lasting for an arbitrarily large number of e-folds. Finally, we explore the effect of anisotropic perturbations onto GFT condensates and show that these are under control at the bounce and become negligible away from it. This also represents a crucial step towards identifying cosmological anisotropies within this approach.
Original language | English |
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Award date | 2019 |
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