Optimal strategies: theoretical approaches to the parametrization of the dark energy equation of state

The absence of compelling theoretical model requires the parameterizing the dark energy to probe its properties. The parametrization of the equation of state of the dark energy is a common method. We explore the theoretical optimization of the parametrization based on the Fisher information matrix. As a suitable parametrization, it should be stable at high redshift and should produce the determinant of the Fisher matrix as large as possible. For the illustration, we propose one parametrization which can satisfy both criteria. By using the proper parametrization, we can improve the constraints on the dark energy even for the same data. We also show the weakness of the so-called principal component analysis method.