This study extends the scalar curvature term Formula: see text within the framework of modified gravity, incorporating both the Ricci scalar Formula: see text and the energy-momentum tensor Formula: see text. We explore a specific formulation of Formula: see text gravity, defined as Formula: see text, in the context of a spatially homogeneous and anisotropic Bianchi type-I cosmological model with a perfect fluid. Within this framework, we derive and analyze the modified field equations for both positive and negative values of Formula: see text. By utilizing observational datasets, we constrain the model parameters and visualize its cosmological implications. Our findings show that for negative Formula: see text, the model remains stable and aligns with physical expectations. However, for positive Formula: see text, anomalous behavior emerges in specific intervals. Furthermore, we validate our model through metric perturbation analysis and cosmological diagnostic tools like Formula: see text and Formula: see text. The combined analysis of EC and observational diagnostics confirms the physical viability and late-time accelerated expansion behavior of the model within the admissible parameter range.
Sharma et al. (Thu,) studied this question.