Dark matter-dark energy interaction for a time-dependent EoS parameter

In this work we investigate the interaction between dark matter and dark energy for a coupling that obeys the Wang-Meng decaying law, rho(DM) proportional to (1 + z)(3-epsilon), and the Barboza-Alcaniz dark energy parametric model, w = w(0) + w(0)'z(1+ z)/(1+ z(2)). Theoretically, we show that the coupling constant, epsilon, should satisfy the physical constraint epsilon >= 0. We use the most recent data of type Ia supernovae, baryon acoustic oscillations, cosmic microwave background and the Hubble expansion rate function to constrain the free parameters of the model. From a purely observational point of view, we show that is not possible to discard values of the coupling constant in the unphysical region epsilon < 0. We show that the uncoupled case, epsilon = 0, is in better agreement with the data than any of coupled models in the physical region. We also find that all physically acceptable interaction in dark sector lies in the narrow range 0 < epsilon <= 0.034 (95% CL).