Viscous fluid with neutrino in f(R,?,X) gravity

In this study, we investigate the Kantowski-Sachs space-time within the framework of f(R,Phi,X) gravity, incorporating a general fluid distribution with neutrino contributions. The field equations are constructed using a hybrid f(R,Phi,X) function that combines features of the Starobinsky-like model and k-essence functions with canonical scalar fields. Analytical solutions are obtained, showing that the fluid can exhibit bulk viscous behavior with neutrino contributions. The model's kinematical properties and energy conditions are investigated. NEC, WEC and DEC are satisfied, while SEC is violated, indicating scenarios where gravity repels matter, enabling exotic configurations. These results provide insights into the early universe's dynamics and the role of viscous fluids and neutrinos in modified gravity theories.