Diego H. Gugliotta | Searcharxiv

arXiv2026

Global variables and dynamics of emergent cosmology in loop gravity

Deriving emergent cosmology from the discrete geometry of Loop Quantum Gravity remains an open challenge. We solve the two-vertex model exactly, including general non-symmetric configurations, by introducing macroscopic global variables that form a closed Poisson subalgebra. This yields an intrinsic minimal area gap from the Casimir invariants of the subalgebra. In the semiclassical limit, a generalized Friedmann equation emerges incorporating graph anisotropies and quantum geometry corrections, which lead to a Big Bounce. This global formulation opens a coarse-graining route toward statistical descriptions of quantum spacetime.

gr-qc↗

arXiv2025

The two-vertex model of loop quantum gravity: anisotropic reduced sectors

The so-called two-vertex model of loop quantum gravity has been analytically studied in the past within a U($N$) symmetry-reduced sector leading to a cosmological interpretation. In this work we study the simplest non-trivial two-vertex model (with four edges, i.e., $N=4$), using the spinorial formalism and twisted geometries to isolate the degrees of freedom and derive a canonical parametrization. We identify eight geometric parameters describing the polyhedral configurations and four twist angles characterizing the system's dynamics. Going beyond the U($N$) symmetry-reduced sector which can be interpreted as homogeneous and isotropic, we find three additional stable symmetry-reduced sectors: the privileged-direction sector, the bi-twist sector, and the inhomogeneous bi-twist sector. Each sector introduces degrees of anisotropy or inhomogeneity and expand the potential cosmological interpretations of the two-vertex model.

gr-qc↗