Bulk viscous cosmological model with varying deceleration parameter in modified gravity

This work investigates a spatially homogeneous and anisotropic Bianchi type-I universe within the framework of [Formula: see text] gravity, where [Formula: see text] is the Ricci scalar and [Formula: see text] represents the trace of the energy–momentum tensor, specifically for the case [Formula: see text]2[Formula: see text], with [Formula: see text] bT. The model employs a specific gravitational function that incorporates bulk viscous matter. A novel, time-dependent deceleration parameter is introduced, extending the form proposed by Tiwari and Sofuoglu (Quadratically varying deceleration parameter in [Formula: see text]([Formula: see text])gravity, Int. J. Geom. Methods Mod. Phys.17 (2020) 2030003). The research focuses on a locally rotationally symmetric (LRS) Bianchi type-I bulk viscous fluid model, which describes the evolution of the universe from an early decelerating phase to its present accelerated expansion. Exact solutions of the field equations are derived using the proposed deceleration parameter, and both the physical and kinematic properties are analyzed in detail and presented graphically. Furthermore, the validity of the weak, dominant, and strong energy conditions, along with the evolution of energy density, is examined. The results indicate that bulk viscosity plays a crucial role in driving the current accelerated expansion of the universe.