Anisotropic Transition Cosmology Driven by Bulk Viscosity and Gaussian Expansion Dynamics

In this paper, we have investigated an anisotropic LRS Bianchi type-I cosmological model filled with a bulk viscous fluid in the framework of f(R, T) gravity. We have consider the linear functional form f(R, T)=R+2λT,

where λ denotes the matter–geometry coupling parameter. To obtain the exact cosmological model solutions, a novel Gaussian-type transition ansatz, e^{∫q/a da} =1/[a√α+βe(-ma*2)],

where α, β, and m are positive constants, is introduced. The proposed ansatz provides a smooth description of the cosmic transition from an early decelerated expansion phase to the present accelerated epoch. Exact expressions for the deceleration parameter, Hubble parameter, expansion scalar, shear scalar, energy density, effective pressure, bulk viscosity coefficient, jerk parameter, and statefinder diagnostics and transition time are derived and analyzed. The physical behavior of the model shows that the energy density remains positive throughout the cosmic evolution, while the bulk viscous effects generate a negative effective pressure that drives late-time acceleration. The anisotropy decreases with cosmic time, indicating a gradual approach toward isotropy. Furthermore, the model evolves asymptotically toward a de-Sitter phase and reproduces the standard ΛCDM statefinder limit (r,s)=(1,0). Therefore, the obtained model provides a physically viable and observationally consistent framework for studying transition cosmology and accelerated expansion in modified gravity.