A Comparison of Thawing and Freezing Dark Energy Parametrizations

Dark energy equation of state $w(z)$ parametrizations with two parameters and given monotonicity are generically either convex or concave functions. This makes them suitable for fitting either freezing or thawing quintessence models but not both simultaneously. Fitting a dataset based on a freezing model with an unsuitable (concave when increasing) $w(z)$ parametrization (like CPL) can lead to significant misleading features like crossing of the phantom divide line, incorrect $w(z=0)$, incorrect slope \etc that are not present in the underlying cosmological model. To demonstrate this fact we generate scattered cosmological data both at the level of $w(z)$ and the luminosity distance $D_L(z)$ based on either thawing or freezing quintessence models and fit them using parametrizations of convex and of concave type. We then compare statistically significant features of the best fit $w(z)$ with actual features of the underlying model. We thus verify that the use of unsuitable parametrizations can lead to misleading conclusions. In order to avoid these problems it is important to either use both convex and concave parametrizations and select the one with the best $\chi^2$ or use principal component analysis thus splitting the redshift range into independent bins. In the latter case however, significant information about the slope of $w(z)$ at high redshifts is lost. Finally, we propose a new family of parametrizations (nCPL) $w(z)=w_0+w_a (\frac{z}{1+z})^n$ which generalizes the CPL and interpolates between thawing and freezing parametrizations as the parameter $n$ increases to values larger than 1.