Effective relational cosmological dynamics from quantum gravity

Abstract

We discuss the relational strategy to solve the problem of time in quantum gravity and different ways in which it could be implemented, pointing out in particular the fundamentally new dimension that the problem takes in a quantum gravity context in which spacetime and geometry are understood as emergent. We realize concretely the relational strategy we have advocated in the context of the tensorial group field theory formalism for quantum gravity, leading to the extraction of an effective relational cosmological dynamics from quantum geometric models. We analyze in detail the emergent cosmological dynamics, highlighting the improvements over previous work, the contribution of the quantum properties of the relational clock to it, and the interplay between the conditions ensuring a bona fide relational dynamics throughout the cosmological evolution and the existence of a quantum bounce resolving the classical big bang singularity.

Quantum gravity states, entanglement graphs and second-quantized tensor networks

“…Operationally, we use these additional degrees of freedom to break the symmetry over the vertex-labels at an effective level only, achieving distinguishability only for a special class of quantum states and in a physically motivated approximation. For simplicity we consider, as additional degrees of freedom, a minimally coupled free massless scalar field λ discretized along the geometric data on the graphs (and simplicial complexes) associated to GFT quantum states, in analogy with the approach of [43,56] for defining a relational dynamics in the GFT condensate cosmology, and based on the analysis of scalar matter coupled to quantum gravity in GFT [57] and canonical LQG and spin foam models [58,59]. The GFT field thus turns into φ(g, λ) ∈ L 2 (G d /G×R), and the canonical commutation relations of eq.…”

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

“…For instance, coupling (free, massless) scalar fields to the geometric degrees of freedom results in the addition of R-valued local variables to the domain of the group field [52][53][54]. Besides making the models more realistic, matter (in particular, scalar) fields can be naturally used to set up a material reference frame, allowing for a simple relational description (at least at an effective, continuum level [52,54,55]) of the evolution of geometric quantities.…”

“…Although non-Euclidean signatures may be important for cosmological applications of these models (see e.g. [52,55]), using a Euclidean signature is customary for applications of mean-field theory to statistical systems, and guarantees that the uniform mean-field configuration, which we will employ below, indeed minimizes the action. Thus we stick to this simplifying choice.…”

“…(2.9) we only include terms of the aforementioned series with the lowest number of derivatives. Such a derivative truncation has been for instance shown to be justified in models where the matter degrees of freedom are used as material reference frames [55].…”

“…Further potential extensions of the method presented here could involve the relaxation of one of its main assumptions which is the projection onto uniform field configurations and to study the behavior of fluctuations around non-uniform minimizers [84][85][86][87][88] of TGFT models, which thus would retain non-local geometric information already in the structure of the non-trivial vacua and not merely in the fluctuations thereon. 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.…”