Dynamics of the Mixmaster Universe in a non-commutative Generalized Uncertainty Principle framework
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866915224210112512 |
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| author | Segreto, Sebastiano Montani, Giovanni |
| author_facet | Segreto, Sebastiano Montani, Giovanni |
| contents | In this work, we examine the dynamical aspects of the cosmological Mixmaster model within the framework of non-commutative generalized uncertainty principle (GUP) theories. The theory is formulated classically by introducing a well-defined symplectic form that differs from the ordinary one, thereby inducing a general deformation of the Poisson brackets describing a precise class of GUP theories. In this general setting, we first investigate the behavior of the Bianchi I and Bianchi II models using Misner variables. Then, we study the Bianchi IX model in the Mixmaster approximation, which is well-known for accurately reproducing the dynamics of the point-particle Universe approaching the cosmological singularity. We derive the corresponding Belinsky-Khalatnikov-Lifshitz (BKL) map and then, by selecting a specific GUP model associated with string theory, we explicitly investigate its resulting features shaped by the non-commutative GUP scheme. Our findings reveal that the chaotic and ergodic behavior typically observed in the standard BKL map, which characterizes the point-Universe's approach to the singularity, is replaced by quasi-periodic orbits in the parameter space of the theory. This corresponds to an oscillatory behavior of the Universe's scale factors, dependent on the initial conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of the Mixmaster Universe in a non-commutative Generalized Uncertainty Principle framework Segreto, Sebastiano Montani, Giovanni General Relativity and Quantum Cosmology High Energy Physics - Theory In this work, we examine the dynamical aspects of the cosmological Mixmaster model within the framework of non-commutative generalized uncertainty principle (GUP) theories. The theory is formulated classically by introducing a well-defined symplectic form that differs from the ordinary one, thereby inducing a general deformation of the Poisson brackets describing a precise class of GUP theories. In this general setting, we first investigate the behavior of the Bianchi I and Bianchi II models using Misner variables. Then, we study the Bianchi IX model in the Mixmaster approximation, which is well-known for accurately reproducing the dynamics of the point-particle Universe approaching the cosmological singularity. We derive the corresponding Belinsky-Khalatnikov-Lifshitz (BKL) map and then, by selecting a specific GUP model associated with string theory, we explicitly investigate its resulting features shaped by the non-commutative GUP scheme. Our findings reveal that the chaotic and ergodic behavior typically observed in the standard BKL map, which characterizes the point-Universe's approach to the singularity, is replaced by quasi-periodic orbits in the parameter space of the theory. This corresponds to an oscillatory behavior of the Universe's scale factors, dependent on the initial conditions. |
| title | Dynamics of the Mixmaster Universe in a non-commutative Generalized Uncertainty Principle framework |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.20476 |