Conformal and Non-Minimal Couplings in Fractional 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_ | 1866916234844438528 |
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| author | Marroquín, Kevin Leon, Genly Millano, Alfredo D. Michea, Claudio Paliathanasis, Andronikos |
| author_facet | Marroquín, Kevin Leon, Genly Millano, Alfredo D. Michea, Claudio Paliathanasis, Andronikos |
| contents | Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases where the power law is observed accurately. Fractional calculus must reflect non-local, frequency- and history-dependent properties of power-law phenomena. This tool has various important applications, such as fractional mass conservation, electrochemical analysis, groundwater flow problems, and fractional spatiotemporal diffusion equations. It can also be used in cosmology to explain late-time cosmic acceleration without the need for dark energy. We review some models using fractional differential equations. We look at the Einstein--Hilbert action, which is based on a fractional derivative action, and add a scalar field, $ϕ$, to create a non-minimal interaction theory with the coupling, $ξR ϕ^2 $, between gravity and the scalar field, where $ξ$ is the interaction constant. By employing various mathematical approaches, we can offer precise schemes to find analytical and numerical approximations of the solutions. Moreover, we comprehensively study the modified cosmological equations and analyze the solution space using the theory of dynamical systems and asymptotic expansion methods. This enables us to provide a qualitative description of cosmologies with a scalar field based on fractional calculus formalism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_13850 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal and Non-Minimal Couplings in Fractional Cosmology Marroquín, Kevin Leon, Genly Millano, Alfredo D. Michea, Claudio Paliathanasis, Andronikos General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases where the power law is observed accurately. Fractional calculus must reflect non-local, frequency- and history-dependent properties of power-law phenomena. This tool has various important applications, such as fractional mass conservation, electrochemical analysis, groundwater flow problems, and fractional spatiotemporal diffusion equations. It can also be used in cosmology to explain late-time cosmic acceleration without the need for dark energy. We review some models using fractional differential equations. We look at the Einstein--Hilbert action, which is based on a fractional derivative action, and add a scalar field, $ϕ$, to create a non-minimal interaction theory with the coupling, $ξR ϕ^2 $, between gravity and the scalar field, where $ξ$ is the interaction constant. By employing various mathematical approaches, we can offer precise schemes to find analytical and numerical approximations of the solutions. Moreover, we comprehensively study the modified cosmological equations and analyze the solution space using the theory of dynamical systems and asymptotic expansion methods. This enables us to provide a qualitative description of cosmologies with a scalar field based on fractional calculus formalism. |
| title | Conformal and Non-Minimal Couplings in Fractional Cosmology |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2402.13850 |