Authors:	Ferrero, Renata
Title:	Nonperturbative quantum dynamics on the de sitter geometry and diffeomorphism-invariant observables
Online publication date:	15-Jan-2024
Year of first publication:	2024
Language:	english
Abstract:	In Quantum Gravity functional integral approaches attempt to give meaning and nonperturbatively evaluate the sum over histories represented by the gravitational path integral. A variant of this approach proceeds indirectly by re-constructing the sought-for functional integral in the continuum limit from the solution of an appropriate Functional Renormalization Group (FRG) equation. This line of thought is at the core of the Asymptotic Safety scenario, in which the UV completion of Quantum Gravity is realized via a non-trivial fixed point of the FRG flow. In the first Part of this thesis, we investigate nonperturbative and geometrical aspects of quantum dynamics in de Sitter spacetime, an Einstein space of Lorentzian signature which may be used to model the observed accelerated expansion of the Universe. In this part, three novel lines of research are established. Firstly, we examine the geometrical and dynamical contents of the Renormalization Group (RG) flow in a broader context, such as in connection with a new variant of the AdS/CFT correspondence. Thereby Quantum Einstein Gravity is explored by solving its scale-dependent effective field equa- tions and embedding the family of emerging 4-dimensional de Sitter spacetimes into a single 5-dimensional manifold. Remarkably, we find that there exist only two possible such 5D spacetimes, namely AdS5 and dS5. Secondly, we investigate the consequences of nonperturbative, Background Independent quantization of gravity on the geometry of de Sitter by means of a newly introduced spectral flow method. A first important result reveals the dynamical thinning out of the effective degrees of freedom in the UV, which is at the heart of Asymptotic Safety. Furthermore, evidence is found for a dynamical fragmentation of the effective quantum spacetime in disjoint, sub-horizon size patches. Thirdly, we construct scattering amplitudes in curved spacetime, reflecting the geometric properties of de Sitter spacetime in a novel and nontrivial way. In a fully covariant formalism, we compute the scattering potential of a graviton-mediated scat- tering process involving two very massive scalars at tree level. On Hubble-size scales the potential yields a repulsive force; this can be attributed to the expansion of the de Sitter Universe. Beyond the horizon, the potential vanishes identically. The second Part of this thesis is devoted to a detailed discussion, and actual computation of physical observables in Quantum Gravity. We analyze the special symmetries of gravity, and we perform the first computations of scale-dependent relational observables in asymptotically safe gravity. First, inspired by the modeling of a physical coordinate scaffolding, we construct general effective dynamics for diffeomorphisms of spacetime. Second, we develop the formalism towards the use of running relational observables within Asymptotic Safety: we introduce RG-dependent couplings associated to the observables, and in the spirit of the composite operator formalism, we derive a new flow equation for these observables. We investigate their scale dependence by computing their critical exponents, carrying out the analysis both in the standard and in the minimal essential renormalization scheme. The (small) quantum corrections encoded in the critical exponents represent universal quantities which can be compared to results from other approaches to Quantum Gravity.
DDC:	530 Physik 530 Physics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-9879
URN:	urn:nbn:de:hebis:77-openscience-ff0a0356-dd3a-4e26-b9d5-79331de8aa080
Version:	Original work
Publication type:	Dissertation
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Extent:	xi, 435 Seiten ; Illustrationen, Diagramme
Appears in collections:	JGU-Publikationen