论文标题
$ f（r）$重力中的超几何可行模型
Hypergeometric viable models in $f(R)$ gravity
论文作者
论文摘要
从需要对$λ$ CDM的动态性，$ f（r）$曲线中存在的拐点以及相位空间曲线$（m $ $ r $ r $ r $具有特征性的型号的拐点条件），在宇宙学上可行的超几何模型$ f（r）$是从对$λ$ cdm的需求，在$ f（r）$曲线中存在的拐点，以及具有相位空间曲线$（m $ r）所给出的可行性条件的条件。为了分析与生存力要求相关的约束，模型是根据无量纲变量表示的，即$ r \ to x $ to x $和$ f（r）\ to y（x）= x+h（x）+λ$，其中$ h（x）$代表模型与一般相关性的偏差。使用拐点施加的几何特性，构建了差异方程式以将$ h'（x）$和$ h''（x）$相关联，并且发现的解决方案是Starobinsky（2007）和Hu-Sawicki类型的模型，尽管如此，这些模型仍然是，这些差异方程式是超细差分方程的特殊情况，因此可以从这些模型中进行特定的型号，因此可以根据这些模型进行A型模型。分析了该模型的参数域以使模型可行。
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.
