Cosmic Expansion of the Universe Characterized by Anisotropic Viscous Fluid Cosmological Models

In this paper, the cosmic expansion of the universe filled with viscous fluid has been discussed in Bianchi type-I space-time. To solve Einstein's field equations, a time-varying deceleration parameter, (q(t)) yields a time variable scale factor a(t) = [\sinh(\alpha t)]^{\frac{1}{n}}, with `\alpha' and `n' are positive constants. We also consider a time-varying gravitational constant (G) via the formulation 8\pi G = G_{0}a^{m}, where `G_{0}' and `m' are positive constants. Further, based on the third constraint, two different viscous cosmological models, one by considering the perfect gas equation of state p=\omega \rho and the other by considering time-varying bulk viscosity coefficient (\xi(t)), have been constructed. It is mentioned here that this particular choice of scale factor generates a class of accelerating models for n<1 while for n > 1, the transition of the universe from early deceleration to current acceleration takes place. An important feature of the models is decreasing dark energy candidate, i.e., cosmological constant (\Lambda) with time, fine-tuning with the results from recent supernovae Ia observations. The various physical parameters involved in the models have been discussed analytically and graphically and are found in good agreement with recent observations. For the physical acceptability of both the models, energy conditions are shown graphically. The models are found to be physically acceptable, particularly in identifying the universe's transition. We have discussed the statefinder and observed that all the trajectories indicate dark energy candidates as Chaplying gas and quintessence for different constraints (\alpha, n). We have also calculated the cosmographic parameters such as jerk, lerk, maxout to analyze the physical behavior of the DE models.