Supernova constraints on alternative models to dark energy

The recent observations of type Ia supernovae suggest that the universe is accelerating now and decelerated in the recent past. This may be the evidence of the breakdown of the standard Friedmann equation. The Friedmann equation $H^2\sim \rho$ is modified to be a general form $H^2=g(\rho )$. Three models with particular form of $g(\rho )$ are considered in detail. The supernova data published by \citet{tonry}, \citet{ddsg} and \citet{raknop03} are used to analyze the models. After the best fit parameters are obtained, we then find out the transition redshift $z_{\mathrm{T}}$ when the universe switched from the deceleration phase to the acceleration phase.