Observational constraints on dark energy model
  The recent observations support that our universe is flat and expanding with acceleration. A quintessence model with a general relation between the quintessence potential and the quintessence kinetic energy was proposed to explain the phenomenon. The dark energy potential includes both the hyperbolic and the double exponential potentials. We analyze this model in detail by using the recent supernova and the first year Wilkinson Microwave Anisotropy Probe (WMAP) observations. For a flat universe dominated by a dark energy with constant $\omega$ which is a special case of the general model, we find that $\Omega_{\rm m0}=0.30^{+0.06}_{-0.08}$ and $\omega_{\rm Q}\le -0.82$, and the turnaround redshift $z_{\rm T}$ when the universe switched from the deceleration phase to the acceleration phase is $z_{\rm T}=0.65$. For the general model, we find that $\Omega_{\rm m0}\sim 0.3$, $\omega_{\rm Q0}\sim -1.0$, $\beta\sim 0.5$ and $z_{\rm T}\sim 0.67$. A model independent polynomial parameterization is also considered, the best fit model gives $\Omega_{\rm m0}=0.40\pm 0.14$, $\omega_{\rm Q0}=-1.4$ and $z_{\rm T}=0.37$. 
Yungui Gong