New analytic solutions in $f\left( R\right) $-Cosmology from Painlevé analysis
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914728066940928 |
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| author | Leon, Genly Paliathanasis, A. Leach, P. G. L. |
| author_facet | Leon, Genly Paliathanasis, A. Leach, P. G. L. |
| contents | Using the singularity analysis, we investigate the integrability properties and existence of analytic solutions in $f\left( R\right)$-cosmology. Specifically, for some power-law $f\left( R\right) $-theories of particular interest, we apply the ARS algorithm to prove if the field equations possess the Painlevé property. Constraints for the free parameters of the power-law models are derived, and new analytic solutions are derived, expressed in terms of Laurent expansions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_01363 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | New analytic solutions in $f\left( R\right) $-Cosmology from Painlevé analysis Leon, Genly Paliathanasis, A. Leach, P. G. L. General Relativity and Quantum Cosmology Mathematical Physics Exactly Solvable and Integrable Systems Using the singularity analysis, we investigate the integrability properties and existence of analytic solutions in $f\left( R\right)$-cosmology. Specifically, for some power-law $f\left( R\right) $-theories of particular interest, we apply the ARS algorithm to prove if the field equations possess the Painlevé property. Constraints for the free parameters of the power-law models are derived, and new analytic solutions are derived, expressed in terms of Laurent expansions. |
| title | New analytic solutions in $f\left( R\right) $-Cosmology from Painlevé analysis |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2205.01363 |