Constraining a scalar field dark energy with variable equation of state for matter

The red-shift $z_{eq}$, marking the end of radiation era and the beginning of matter-dominated era, can play an important role to reconstruct dark-energy models. A variable equation of state for matter that can bring a smooth transition from radiation to matter-dominated era in a single model is proposed to estimate $z_{eq}$ in dark energy models and hence its viability. Two one-parameter models with minimally coupled scalar fields playing the role of dark energy are chosen to demonstrate this point. It is found that for desired late time behavior of the models, the estimated value of $z_{eq}$ is highly sensitive on the value of the parameter in each of these models.