$f(R,\square R)$-gravity and equivalency with the modified GUP Scalar field models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916196379525120 |
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| author | Paliathanasis, Andronikos |
| author_facet | Paliathanasis, Andronikos |
| contents | Inspired by the generalization of scalar field gravitational models with a minimum length we study the equivalent theory in modified theories of gravity. The quadratic Generalized Uncertainty Principle (GUP) gives rise to a deformed Heisenberg algebra in the application, resulting in the emergence of additional degrees of freedom described by higher-order derivatives. The new degrees of freedom can be attributed to the introduction of a new scalar field, trasforming the resulting theory into a two-scalar field theory. Thus, in order to describe all the degrees of freedom we investigate special forms of the sixth-order modify $f\left( R,\square R\right) -$theory of gravity, where the gravitational Lagrangian has similar properties~to~that of the GUP scalar field theory. Finally, the cosmological applications are discussed, and we show that the de Sitter universe can be recovered without introducing a cosmological constant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_04519 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $f(R,\square R)$-gravity and equivalency with the modified GUP Scalar field models Paliathanasis, Andronikos General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Inspired by the generalization of scalar field gravitational models with a minimum length we study the equivalent theory in modified theories of gravity. The quadratic Generalized Uncertainty Principle (GUP) gives rise to a deformed Heisenberg algebra in the application, resulting in the emergence of additional degrees of freedom described by higher-order derivatives. The new degrees of freedom can be attributed to the introduction of a new scalar field, trasforming the resulting theory into a two-scalar field theory. Thus, in order to describe all the degrees of freedom we investigate special forms of the sixth-order modify $f\left( R,\square R\right) -$theory of gravity, where the gravitational Lagrangian has similar properties~to~that of the GUP scalar field theory. Finally, the cosmological applications are discussed, and we show that the de Sitter universe can be recovered without introducing a cosmological constant. |
| title | $f(R,\square R)$-gravity and equivalency with the modified GUP Scalar field models |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2404.04519 |