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 \sim 0.7 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 .