Abstract
We analyze the size and evolution of quantum fluctuations of cosmologically relevant geometric observables, in the context of the effective relational cosmological dynamics of GFT models of quantum gravity. We consider the fluctuations of the matter clock observables, to test the validity of the relational evolution picture itself. Next, we compute quantum fluctuations of the universe volume and of other operators characterizing its evolution (number operator for the fundamental GFT quanta, effective Hamiltonian and scalar field momentum). In particular, we focus on the late (clock) time regime, where the dynamics is compatible with a flat FRW universe, and on the very early phase near the quantum bounce produced by the fundamental quantum gravity dynamics.
Highlights
Three closely related challenges have to be overcome by fundamental quantum gravity approaches, especially those based on discrete or otherwise non-geometric, non-spatiotemporal entities, in order to make contact with General Relativity and observed gravitational physics, based on effective field theory
This construction is motivated by the argued usefulness and conceptual importance of effective approaches to relational dynamics (Bojowald et al, 2009; Bojowald and Tsobanjan, 2009; Bojowald et al, 2011a; Bojowald et al, 2011b; Bojowald, 2012), and it was suggested a general framework in which the latter is realized in a “tempus post quantum” approach, but only at a proto-geometric level, i.e. after some suitable coarse graining, the one provided by the group field theory (GFT) hydrodynamic approximation. This effective relational framework improves on previous relational constructions in GFT cosmology providing a mathematically more solid definition of relational observables, allowing the explicit computation of quantum fluctuations, which will be one the main objectives of the present work. This improved effective relational dynamics was obtained by the use of “Coherent Peaked States” (CPSs), in which the fundamental GFT quanta collectively reproduce the classical notion of a spacelike slice of a spacetime foliation labeled by a massless scalar field clock
The purpose of this paper is to explore under which conditions this averaged relational dynamics is meaningful and captures the relevant physics, checking quantum fluctuation for both clock observables and cosmological, geometric ones
Summary
Three closely related challenges have to be overcome by fundamental quantum gravity approaches, especially those based on discrete or otherwise non-geometric, non-spatiotemporal entities, in order to make contact with General Relativity and observed gravitational physics, based on effective (quantum) field theory. The first is the continuum limit/approximation leading from the fundanental entities and their quantum dynamics to an effective continuum description of spacetime and geometry, with matter fields living on it (Oriti et al, 2017) This requires a mixture of renormalization analysis of the fundamental quantum dynamics and of coarse-graining of its states and observables. This effective relational framework improves on previous relational constructions in GFT cosmology providing a mathematically more solid definition of relational observables, allowing the explicit computation of quantum fluctuations, which will be one the main objectives of the present work This improved effective relational dynamics was obtained by the use of “Coherent Peaked States” (CPSs), in which the fundamental GFT quanta collectively (and only effectively) reproduce the classical notion of a spacelike slice of a spacetime foliation labeled by a massless scalar field clock. The purpose of this paper is to explore under which conditions this averaged relational dynamics is meaningful and captures the relevant physics, checking quantum fluctuation for both clock observables and cosmological, geometric ones
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