Classical and Quantum solutions in Scalar field cosmology via the Eisenhart lift and linearization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910294574366720 |
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| author | Paliathanasis, Andronikos |
| author_facet | Paliathanasis, Andronikos |
| contents | This study introduces a novel approach for solving the cosmological field equations within scalar field theory by employing the Eisenhart lift. The field equations are reformulated as a system of geodesic equations for the Eisenhart metric. In the case of an exponential potential, the Eisenhart metric is shown to be conformally flat. By applying basic geometric principles, a new set of dynamical variables is identified, allowing for the linearization of the field equations and the derivation of classical cosmological solutions. However, the quantization of the Eisenhart system reveals a distinct set of solutions for the wavefunction, particularly in the presence of symmetry breaking at the quantum level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05775 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical and Quantum solutions in Scalar field cosmology via the Eisenhart lift and linearization Paliathanasis, Andronikos General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Mathematical Physics This study introduces a novel approach for solving the cosmological field equations within scalar field theory by employing the Eisenhart lift. The field equations are reformulated as a system of geodesic equations for the Eisenhart metric. In the case of an exponential potential, the Eisenhart metric is shown to be conformally flat. By applying basic geometric principles, a new set of dynamical variables is identified, allowing for the linearization of the field equations and the derivation of classical cosmological solutions. However, the quantization of the Eisenhart system reveals a distinct set of solutions for the wavefunction, particularly in the presence of symmetry breaking at the quantum level. |
| title | Classical and Quantum solutions in Scalar field cosmology via the Eisenhart lift and linearization |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Mathematical Physics |
| url | https://arxiv.org/abs/2401.05775 |