Bohmian Quantization of a Nonminimal Coupling Cosmology
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913535415549952 |
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| author | Torres, Isaac Santos, Felipe de Melo da Piedade, Anderson Almeida |
| author_facet | Torres, Isaac Santos, Felipe de Melo da Piedade, Anderson Almeida |
| contents | In a recent paper we studied the cosmology of Nonminimal Derivative Coupling (NDC) between gravity and a scalar field, which is a non-trivial class of Horndeski. We have shown that it presents a variety of solutions for the scale factor, but there are gravitational waves only for a very restrictive range in phase space, and primordial waves are completely forbidden classically in NDC. In this paper, we apply canonical quantization with the Bohm-de Broglie interpretation to that theory for a small value of the nonminimal coupling constant. We then study two quantum solutions of the Wheeler-DeWitt equation that lead to the perturbation of bouncing and cyclic solutions. By the analysis of the phase space obtained from the guidance equations of Bohm-de Broglie, we study the phase space determined by the scale factor and the scalar field for those quantum solutions in order to investigate three main aspects of that theory: the existence of non-singular solutions, the regions of accelerated expansion, and the regions compatible with the gravitational waves speed constraint. We conclude that there are non-singular solutions with an accelerated expansion period compatible with the constraint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04624 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bohmian Quantization of a Nonminimal Coupling Cosmology Torres, Isaac Santos, Felipe de Melo da Piedade, Anderson Almeida General Relativity and Quantum Cosmology In a recent paper we studied the cosmology of Nonminimal Derivative Coupling (NDC) between gravity and a scalar field, which is a non-trivial class of Horndeski. We have shown that it presents a variety of solutions for the scale factor, but there are gravitational waves only for a very restrictive range in phase space, and primordial waves are completely forbidden classically in NDC. In this paper, we apply canonical quantization with the Bohm-de Broglie interpretation to that theory for a small value of the nonminimal coupling constant. We then study two quantum solutions of the Wheeler-DeWitt equation that lead to the perturbation of bouncing and cyclic solutions. By the analysis of the phase space obtained from the guidance equations of Bohm-de Broglie, we study the phase space determined by the scale factor and the scalar field for those quantum solutions in order to investigate three main aspects of that theory: the existence of non-singular solutions, the regions of accelerated expansion, and the regions compatible with the gravitational waves speed constraint. We conclude that there are non-singular solutions with an accelerated expansion period compatible with the constraint. |
| title | Bohmian Quantization of a Nonminimal Coupling Cosmology |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2410.04624 |