Investigating the Possibility of a Turning Point in the Dark Energy Equation of State

We investigate a second order $parabolic$ parametrization, $w(a)=w_t+w_a(a_t-a)^2$, which is a direct characterization of a possible $turning$ in $w$. The cosmological consequence of this parametrization is explored by using the observational data of the SNLS3 type Ia supernovae sample, the CMB measurements from WMAP9 and Planck, the Hubble parameter measurement from HST, and the baryon acoustic oscillation (BAO) measurements from 6dFGS, BOSS DR11 and improved WiggleZ. We found the existence of a turning point in $w$ at $a\sim0.7$ is favored at 1$\sigma$ CL. In the epoch $0.55< a< 0.9$, $w<-1$ is favored at 1$\sigma$ CL, and this significance increases near $a=0.8$, reaching a 2$\sigma$ CL. The parabolic parametrization achieve equivalent performance to the $\Lambda$CDM and Chevallier-Polarski-Linder (CPL) models when the Akaike information criterion was used to assess them. Our analysis shows the value of considering high order parametrizations when studying the cosmological constraints on $w$.