We deepen the analysis of the cosmological acceleration produced by quantum gravity dynamics in the formalism of group field theory condensate cosmology, treated at the coarse-grained level via a phenomenological model, in the language of hydrodynamics on minisuperspace. Specifically, we conduct a detailed analysis of the late-time evolution, which shows a phantom-like phase followed by an asymptotic De Sitter expansion. We argue that the model indicates a recent occurrence of the phantom crossing and we extract a more precise expression for the effective cosmological constant, linking its value to other parameters in the model and to the scale of the quantum bounce in the early Universe evolution. Additionally, we show how the phantom phase produced by our quantum gravity dynamics increases the inferred value of the current Hubble parameter based on observed data, indicating a possible quantum gravity mechanism for alleviating the Hubble tension. Our results represent a concrete example of how quantum gravity can provide an explanation for large-scale cosmological puzzles, in an emergent spacetime scenario.

We present a set of noncommuting tetrad-shift symmetries in 4D gravity in tetrad-connection variables, which allow expressing diffeomorphisms as composite transformations. Working on the phase space level for finite regions, we pay close attention to the corner piece of the generators, discuss various possible charge brackets, relative definitions of the charges, coupling to spinors and relations to other charges. What emerges is a picture of the symmetries and edge modes of gravity that bears local resemblance to a Poincare group SO(1,3)(sic)R-1,R-3, but possesses structure functions. In particular, we argue that the symmetries and charges presented here are more amenable to discretisation, and sketch a strategy for this charge algebra, geared toward quantum gravity applications.

"This collection of perspective pieces captures recent advancements and reflections from a dynamic research community dedicated to bridging quantum gravity, hydrodynamics, and emergent cosmology. It explores four key research areas: (a) the interplay between hydrodynamics and cosmology, including analog gravity systems,. (b) phase transitions, continuum limits and emergent geometry in quantum gravity,. (c) relational perspectives in gravity and quantum gravity,. and (d) the emergence of cosmological models rooted in quantum gravity frameworks. Each contribution presents the distinct perspectives of its respective authors. Additionally, the introduction by the editors proposes an integrative view, suggesting how these thematic units could serve as foundational pillars for a novel theoretical cosmology framework termed ""hydrodynamics on superspace""."

We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data, in the form of generalized tensor networks. This class specifically includes spin networks, the kinematic states of lattice gauge theory, and discrete quantum gravity. We employ an algebraic, operatorial definition of holography based on quantum information channels, an approach which is particularly valuable in settings, such as the one we consider, where the relevant Hilbert space of states does not factorize into subsystem Hilbert spaces due to gauge invariance. We apply random tensor network techniques (successfully used in the AdS/CFT context) to analyze information transport properties of the bulk-to-boundary and boundary-to-boundary maps associated with this superposition of quantum geometries and produce typicality results about the average over the geometric data coloring the fixed graph structure. In this context, one naturally obtains a nontrivial area operator encoding the dominant contribution to entropy calculations. Among our main results is the requirement that one can only isometrically map a bulk region onto boundaries with fixed total area. We furthermore inquire about similar state-induced mappings between segments of the boundary and discuss related conditions for isometric behavior. These generalizations make further steps toward quantum gravity implementations of tensor network holography.

We continue the series of articles on the application of Landau-Ginzburg mean-field theory to unveil the basic phase structure of tensorial field theories which are characterized by combinatorially non-local interactions. Among others, this class covers tensor field theories (TFT) which lead to a new class of conformal field theories highly relevant for investigations on the AdS/CFT conjecture. Moreover, it also encompasses models within the tensorial group field theory (TGFT) approach to quantum gravity. Crucially, in the infrared we find that the effective mass of the modes relevant for the critical behavior vanishes not only at criticality but also throughout the entire phase of non-vanishing vacuum expectation value due to the non-locality of the interactions. As a consequence, one encounters there the emergence of scale invariance on configuration space which is potentially enhanced to conformal invariance thereon.

We consider transition amplitudes in the coloured simplicial Boulatov model for three-dimensional Riemannian quantum gravity. First, we discuss aspects of the topology of coloured graphs with non-empty boundaries. Using a modification of the standard rooting procedure of coloured tensor models, we then write transition amplitudes systematically as topological expansions. We analyse the transition amplitudes for the simplest boundary topology, the 2-sphere, and prove that they factorize into a sum entirely given by the combinatorics of the boundary spin network state and that the leading order is given by graphs representing the closed 3-ball in the large N limit. This is the first step towards a more detailed study of the holographic nature of coloured Boulatov-type GFT models for topological field theories and quantum gravity.

Controlling the continuum limit and extracting effective gravitational physics are shared challenges for quantum gravity approaches based on quantum discrete structures. The description of quantum gravity in terms of tensorial group field theory (TGFT) has recently led to much progress in its application to phenomenology, in particular, cosmology. This application relies on the assumption of a phase transition to a nontrivial vacuum (condensate) state describable by mean-field theory, an assumption that is difficult to corroborate by a full RG flow analysis due to the complexity of the relevant TGFT models. Here, we demonstrate that this assumption is justified due to the specific ingredients of realistic quantum geometric TGFT models: combinatorially nonlocal interactions, matter degrees of freedom, and Lorentz group data, together with the encoding of microcausality. This greatly strengthens the evidence for the existence of a meaningful continuum gravitational regime in group-field and spin-foam quantum gravity, the phenom-enology of which is amenable to explicit computations in a mean-field approximation.

In the tensorial group field theory (TGFT) approach to quantum gravity, the basic quanta of the theory correspond to discrete building blocks of geometry. It is expected that their collective dynamics gives rise to continuum spacetime at a coarse grained level, via a process involving a phase transition. In this work we show for the first time how phase transitions for realistic TGFT models can be realized using Landau-Ginzburg mean-field theory. More precisely, we consider models generating 4-dimensional Lorentzian triangulations formed by spacelike tetrahedra the quantum geometry of which is encoded in non-local degrees of freedom on the non-compact group SL(2,C) and subject to gauge and simplicity constraints. Further we include Double-struck capital R-valued variables which may be interpreted as discretized scalar fields typically employed as a matter reference frame. We apply the Ginzburg criterion finding that fluctuations around the non-vanishing mean-field vacuum remain small at large correlation lengths regardless of the combinatorics of the non-local interaction validating the mean-field theory description of the phase transition. This work represents a first crucial step to understand phase transitions in compelling TGFT models for quantum gravity and paves the way for a more complete analysis via functional renormalization group techniques. Moreover, it supports the recent extraction of effective cosmological dynamics from TGFTs in the context of a mean-field approximation.

The causal structure is a quintessential element of continuum spacetime physics and needs to be properly encoded in a theory of Lorentzian quantum gravity. Established spin foam [and tensorial group field theory (TGFT)] models mostly work with relatively special classes of Lorentzian triangulations (e.g., built from spacelike tetrahedra only) obscuring the explicit implementation of the local causal structure at the microscopic level. We overcome this limitation and construct a full-fledged model for Lorentzian quantum geometry the building blocks of which include spacelike, lightlike, and timelike tetrahedra. We realize this within the context of the Barrett-Crane TGFT model. Following an explicit characterization of the amplitudes via methods of integral geometry and the ensuing clear identification of local causal structure, we analyze the model's amplitudes with respect to its (space)time-orientation properties and provide also a more detailed comparison with the framework of causal dynamical triangulations.