Model independent analysis of dark energy I: Supernova fitting result

The nature of dark energy is a mystery to us. This paper uses the supernova data to explore the property of dark energy by some model independent methods. We first Talyor expanded the scale factor $a(t)$ to find out the deceleration parameter $q_0<0$. This result just invokes the Robertson-Walker metric. Then we discuss several different parameterizations used in the literature. We find that $\Omega_{\rm DE0}$ is almost less than -1 at $1\sigma$ level. We also find that the transition redshift from deceleration phase to acceleration phase is $z_{\rm T}\sim 0.3$.