Quantum Fluctuations in the Effective Relational GFT Cosmology

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.

Generalised effective cosmology from group field theory

“…The fact that quantum fluctuations can be relatively small even when curvature is large is a feature shared with LQC models [31,32]. A crucial property of our approach is that the (averaged) particle number remains constant, as we have emphasised several times above, in sharp contrast to previous results on quantum fluctuations in GFT cosmology [27,28] where the (average) particle number had a non-trivial relational evolution. 17…”

“…In the framework presented in this paper, the number operator is constant because the quantum constraint is a one-body operator and, as such, trivially commutes with the number operator. In most previous attempts to extract cosmological physics from GFT the particle number is time-dependent, and this time dependence can crucially enhance or suppress quantum fluctuations [27,28].…”

Effective relational cosmological dynamics from Quantum Gravity

“…We will then be able to study the relational dynamics of the volume operator, in particular checking whether it matches the classical expectation at least at a certain semi-classical effective level and whether the singularity is resolved at least in terms of expectation values. Before doing that, however, we discuss, in Subsection V D, the validity of the conditions (5), while we discuss the effective relational volume dynamics in Subsection V E. A detailed study of the validity of the conditions (7) will be presented in a forthcoming paper [46].…”

“…However, this "synchronization condition" has to be taken with care. Taking the limit → 0, in fact, would produce [46] arbitrarily large quantum fluctuations on the momentum of the massless scalar field. Such infinite fluctuations can not be of course included in a self-consistent framework implementing a notion effective relational dynamics.…”

Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom

“…Considering nonuniform mean-field configurations also in the local variables could be crucial to connect to cosmological applications of GFTs [39][40][41], where the non-trivial dependence of the meanfield solution on one local variable allows for a relational interpretation of the evolution of geometry with respect to matter degrees of freedom [52,54,55]. The impact of fluctuations in that context has already been studied [89][90][91], but so far only by assuming negligible interactions.…”