Bulk viscous LRS Bianchi type-I cosmology with dynamic vacuum energy: A model for late-time cosmic acceleration

In this study, we explore cosmological models that include bulk viscosity and a decaying vacuum energy density (VED) within an anisotropic, locally rotationally symmetric (LRS) Bianchi type I spacetime. The cosmological constant is expressed in a running-vacuum form as Λ = l H ̇ + ( l + λ ) H 2 + 4 π G η ρ m , where l , λ , and η are dimensionless parameters. The associated vacuum energy density is given by ρ Λ = Λ / ( 8 π G ) , which simplifies to ρ Λ = l H ̇ + ( l + λ ) H 2 + 1 2 η ρ m in natural units where 8 π G = 1 . The viscous pressure is described using the non-causal Eckart theory, and we derive analytical solutions for both the Hubble parameter and the scale factor. We constrain the model parameters through Markov Chain Monte Carlo (MCMC) analysis, utilizing 31 Hubble parameter measurements and 1048 Pantheon supernova data points. Various cosmological parameters are calculated and compared with those from the standard Λ CDM model. Our findings indicate that the model captures the universe’s transition from a matter-dominated decelerating phase to an accelerating phase, as reflected in the behavior of the deceleration and equation-of-state (EoS) parameters. We show that the model is consistent with observational cosmological data and converges to the Λ CDM model at late times. Additionally, we apply model selection criteria such as AIC, BIC and DIC to evaluate the statistical robustness of the model. Overall, this approach provides fresh perspectives on the dynamics of varying vacuum energy density, emphasizing the decaying characteristic of dark energy and its significance in the evolution of the cosmos.