Thermodynamics of Viscous Dark Energy in DGP Setup

Abstract

We investigate thermodynamics of viscous dark energy interacting with dark matter in a DGP braneworld. We show that the Friedmann equation in this setup can be rewritten as the first law of thermodynamics on the apparent horizon. We study the time evolution of the total entropy including the entropy of the matter fields inside the apparent horizon together with the entropy associated with the apparent horizon. Interestingly enough, we find that, in the presence of bulk viscosity, the generalized second law of thermodynamics is always preserved for both branches of the DGP braneworld. When the time varying gravitational constant is taken into account, the generalized second law of thermodynamics can be secured provided \(\dot{G}_{4} \frac{\dot{G}_{4}}{G_{4}}\) and \(\omega_{de}>-1-u+\frac{3H\xi}{\rho_{de}}\), where ξ and u are, respectively, the bulk viscosity coefficient and the energy densities ratio of the two dark components on the brane.