The two-vertex model of loop quantum gravity: anisotropic reduced sectors
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909465378291712 |
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| author | Garay, Iñaki Garay, Luis J. Gugliotta, Diego H. |
| author_facet | Garay, Iñaki Garay, Luis J. Gugliotta, Diego H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The two-vertex model of loop quantum gravity: anisotropic reduced sectors Garay, Iñaki Garay, Luis J. Gugliotta, Diego H. General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | The two-vertex model of loop quantum gravity: anisotropic reduced sectors |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.14352 |