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| Main Authors: | , |
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| Format: | Preprint |
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2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.00297 |
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| _version_ | 1866918007555489792 |
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| author | Hurtado, Roger Arenas, Robel |
| author_facet | Hurtado, Roger Arenas, Robel |
| contents | A cosmologically viable hypergeometric model in the modified gravity theory $f(R)$ is found from the need for asintoticity towards $Λ$CDM, the existence of an inflection point in the $f(R)$ curve, and the conditions of viability given by the phase space curves $(m, r)$, where $m$ and $r$ are characteristic functions of the model. To analyze the constraints associated with the viability requirements, the models were expressed in terms of a dimensionless variable, i.e. $R\to x$ and $f(R)\to y(x)=x+h(x)+λ$, where $h(x)$ represents the deviation of the model from General Relativity. Using the geometric properties imposed by the inflection point, differential equations were constructed to relate $h'(x)$ and $h''(x)$, and the solutions found were Starobinsky (2007) and Hu-Sawicki type models, nonetheless, it was found that these differential equations are particular cases of a hypergeometric differential equation, so that these models can be obtained from a general hypergeometric model. The parameter domains of this model were analyzed to make the model viable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_00297 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hypergeometric viable models in $f(R)$ gravity Hurtado, Roger Arenas, Robel General Relativity and Quantum Cosmology A cosmologically viable hypergeometric model in the modified gravity theory $f(R)$ is found from the need for asintoticity towards $Λ$CDM, the existence of an inflection point in the $f(R)$ curve, and the conditions of viability given by the phase space curves $(m, r)$, where $m$ and $r$ are characteristic functions of the model. To analyze the constraints associated with the viability requirements, the models were expressed in terms of a dimensionless variable, i.e. $R\to x$ and $f(R)\to y(x)=x+h(x)+λ$, where $h(x)$ represents the deviation of the model from General Relativity. Using the geometric properties imposed by the inflection point, differential equations were constructed to relate $h'(x)$ and $h''(x)$, and the solutions found were Starobinsky (2007) and Hu-Sawicki type models, nonetheless, it was found that these differential equations are particular cases of a hypergeometric differential equation, so that these models can be obtained from a general hypergeometric model. The parameter domains of this model were analyzed to make the model viable. |
| title | Hypergeometric viable models in $f(R)$ gravity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2012.00297 |