Li, X (reprint author), Korea Inst Adv Study, Hoegiro 87, Seoul 130722, South Korea.
; Li Miao
; Zhang ZhenHui] Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Beijing 100190, Peoples R China
; [Hu YaZhou
; Zhang ZhenHui] Chinese Acad Sci, Kavli Inst Theoret Phys China, Beijing 100190, Peoples R China
; [Li Miao] Sun Yat Sen Univ, Sch Astron & Space Sci, Guangzhou 510275, Guangdong, Peoples R China
; [Li XiaoDong] Korea Inst Adv Study, Seoul 130722, South Korea
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 similar to 0.7 is favored at l 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 ACDM and Chevallier-Polarski-Linder (CPL) models when the Akailce information criterion was used to assess them. Our analysis shows the value of considering high order parametrizations when studying the cosmological constraints on w.