Scalar field dark energy models with a dynamical equation of state for matter

The red-shift zeq, which signifies the termination of the radiation-dominated epoch and the onset of the matter-dominated era, can serve as an important diagnostic tool in reconstructing dark-energy models. In this work, we introduce a variable equation of state for matter that enables a smooth and continuous transition from radiation domination to matter domination within a single framework. This formulation allows estimation of zeq in dark energy models and thereby facilitates assessment of their viability. To illustrate this approach, two one-parameter models involving minimally coupled scalar fields as dark energy are examined. We find that, although these models successfully reproduce the desired late-time cosmic behavior, the estimated value of zeq exhibits strong sensitivity to the parameter value in each case.