Unimodular JT gravity and de Sitter quantum cosmology
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arXiv
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| Format: | Preprint |
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2025
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| author | Alexandre, Bruno Etkin, Altay Rassouli, Farbod-Sayyed |
| author_facet | Alexandre, Bruno Etkin, Altay Rassouli, Farbod-Sayyed |
| contents | In this work, we show that a gauge-theoretic description of Jackiw-Teitelboim (JT) gravity naturally yields a Henneaux-Teitelboim (HT) unimodular gravity via a central extension of its isometry group, valid for both flat and curved two-dimensional spacetimes. HT gravity introduces a unimodular time canonically conjugate to the cosmological constant, serving as a physical time in quantum cosmology. By studying the mini-superspace reduction of $\text{HT}_2$ gravity, the Wheeler-DeWitt equation becomes a Schrödinger-like equation, giving a consistent and unitary quantum theory. Analysis of the wavefunction's probability density reveals a quantum distribution for the scale factor $a$, offering a quantum perspective on the expansion and contraction of the universe. In this perspective, the possibility of reaching the singular point $a=0$ signals that topology change could occur. Finally, we give a consistent quantum description of unimodular time that aligns seamlessly with Page-Wootters formulation of quantum mechanics, where quantum correlations between unimodular time and JT gravity are studied in $\text{HT}_2$ quantum cosmology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_17213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unimodular JT gravity and de Sitter quantum cosmology Alexandre, Bruno Etkin, Altay Rassouli, Farbod-Sayyed General Relativity and Quantum Cosmology High Energy Physics - Theory In this work, we show that a gauge-theoretic description of Jackiw-Teitelboim (JT) gravity naturally yields a Henneaux-Teitelboim (HT) unimodular gravity via a central extension of its isometry group, valid for both flat and curved two-dimensional spacetimes. HT gravity introduces a unimodular time canonically conjugate to the cosmological constant, serving as a physical time in quantum cosmology. By studying the mini-superspace reduction of $\text{HT}_2$ gravity, the Wheeler-DeWitt equation becomes a Schrödinger-like equation, giving a consistent and unitary quantum theory. Analysis of the wavefunction's probability density reveals a quantum distribution for the scale factor $a$, offering a quantum perspective on the expansion and contraction of the universe. In this perspective, the possibility of reaching the singular point $a=0$ signals that topology change could occur. Finally, we give a consistent quantum description of unimodular time that aligns seamlessly with Page-Wootters formulation of quantum mechanics, where quantum correlations between unimodular time and JT gravity are studied in $\text{HT}_2$ quantum cosmology. |
| title | Unimodular JT gravity and de Sitter quantum cosmology |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.17213 |