Reconstruction of the deceleration parameter and the equation of state of dark energy

The new 182 gold supernova Ia data, the baryon acoustic oscillation measurement and the shift parameter determined from the Sloan Digital Sky Survey, and the three-year Wilkinson Microwave Anisotropy Probe data are combined to reconstruct the dark energy equation of state parameter $w(z)$ and the deceleration parameter $q(z)$. We find that the strongest evidence of acceleration happens around the redshift $z\ensuremath{\sim}0.2$ and the stringent constraints on $w(z)$ lie in the redshift range $z\ensuremath{\sim}0.2--0.5$. At the sweet spot, $\ensuremath{-}1.2<w(z)<\ensuremath{-}0.6$ for the dark energy parametrization $w(z)={w}_{0}+{w}_{a}z/(1+z{)}^{2}$ at the $3\ensuremath{\sigma}$ confidence level. The transition redshift ${z}_{t}$ when the Universe underwent the transition from deceleration to acceleration is derived to be ${z}_{t}={0.36}_{\ensuremath{-}0.08}^{+0.23}$. The combined data is also applied to find out the geometry of the Universe, and we find that at the $3\ensuremath{\sigma}$ confidence level, $|{\ensuremath{\Omega}}_{k}|\ensuremath{\lesssim}0.05$ for the simple one-parameter dark energy model, and $\ensuremath{-}0.064<{\ensuremath{\Omega}}_{k}<0.028$ for the $\ensuremath{\Lambda}\mathrm{CDM}$ model.

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