Unified Non-Singular Cosmology with Late-Time Acceleration through a Novel Parametrization of Bulk Viscosity Coefficient

This work explores the influence of viscous fluids on cosmological dynamics within the framework of General Relativity. We introduce a novel time-dependent parametrization for the bulk viscosity coefficient, given by \(\zeta = \zeta_0 (t - t_0)^{-2n} \rho^{1/2}\), where \(\zeta_0\), \(t_0\), and \(n\) are model parameters. This formulation is designed to investigate whether bulk viscosity of this nature can effectively describe the evolution of the universe, particularly in scenarios that avoid initial singularities through a cosmological bounce. Remarkably, the general solutions emerging from our model exhibit significant flexibility, accommodating not only a bouncing universe but also an early inflationary phase and a late-time acceleration mimicking dark energy. The roles of \(\zeta_0\), \(t_0\), and \(n\) are pivotal, as they govern the cosmic evolution and determine the transitions between different phases. To validate the robustness of our model, we analyze key cosmological quantities such as the energy density, deceleration parameter, and the validity of various energy conditions. Furthermore, we employ statefinder diagnostics to probe the dark energy behavior and examine Hubble flow parameters to shed light on the inflationary aspects of the model. Lastly, we confront our theoretical predictions with observational data sets, including the BAO, DESI and Pantheon+SH0ES datasets, demonstrating the model's consistency with empirical cosmological trends.