Hypergeometric viable models in f(R) gravity

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