Probing bulk viscous matter-dominated model in Brans-Dicke theory

Abstract

We explore a matter-dominated model with bulk viscosity in Brans-Dicke theory to interpret the observed cosmic accelerating expansion phenomena. We obtain the exact solution of the field equations by taking constant bulk viscous coefficient (which potentially could explain the present accelerated expansion of the Universe) and Brans-Dicke scalar field proportional to some power of the scale factor. The model is studied statistically using the available astronomical data and then compare using the tools taken from information criterion. Using the best-fit values of model parameters we find that the model shows transition from decelerated phase to accelerated phase. The effective equation of state parameter is within the quintessence region ($-1\leq \omega <0$). Thus, the model shows quintessence behavior and approaches to $\varLambda $CDM model in late time. It does not cross the phantom divide line and hence it is free from big-rip singularity. The viscous model also alleviates the age problem. We discuss two diagnostic parameters, namely statefinder and $Om(z)$ and compare the model with the existing models by plotting the trajectories. We also apply Akaike information criterion $(\mathit{AIC})$ and Bayesian information criterion $(\mathit{BIC})$ to discriminate the viscous model based on the penalization associated to the number of parameters. The analyses based on the $\mathit{AIC}$ indicates that there is less support for the viscous model when compared to the $\varLambda $CDM model, while those based on the $\mathit{BIC}$ indicates that there is strong evidence against it in favor of the $\varLambda $CDM model.