Hypergeometric viable models in f(R) gravity

Abstract 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 ΛCDM, 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 ) + λ , 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.