Hypergeometric viable models in f(R) gravity

A cosmologically viable hypergeometric model within the framework of the modified gravity theory f(R) has been derived based on the requirements of asymptotic behavior towards Lambda CDM, the presence of an inflection point in the f (R) curve, and the viability conditions dictated by the phase space curves (m, r), where m and r denote characteristic functions of the model. To examine the constraints associated with these viability criteria, the models were expressed in terms of a dimensionless variable, namely R -> x and f (R) -> y(x)= x + h(x) +lambda, where h(x) represents the deviation of the model from General Relativity. By employing the geometric properties imposed by the inflection point, differential equations were formulated to establish the relationship between h'(x) and h ''(x). The resulting solutions yielded models of the Starobinsky (2007) and Hu-Sawicki types. However, it was subsequently discovered that these differential equations correspond to specific cases of a hypergeometric differential equation, indicating that these models can be derived from a more general hypergeometric model. The parameter domains of this model were thoroughly analyzed to ensure its viability.