Time-Varying Dark Energy Constraints From the Latest SN Ia, BAO and SGL
  Based on the latest SNe Ia data provided by Hicken et al. (2009) with using
MLCS17 light curve fitter, together with the Baryon Acoustic Oscillation(BAO)
and strong gravitational lenses(SGL), we investigate the constraints on the
dark energy equation-of-state parameter $w$ in the flat universe, especially
for the time-varying case $w(z)=w_0+w_zz/(1+z)$. The constraints from SNe data
alone are found to be: (a) $(\Omega_M, w)=(0.358, -1.09)$ as the best-fit
results; (b) $(w_0, w_z)=(-0.73^{+0.23}_{-0.97}, 0.84^{+1.66}_{-10.34})$ for
the two parameters in the time-varying case after marginalizing the parameter
$\Omega_M$; (c) the likelihood of parameter $w_z$ has a high non-Gaussian
distribution; (d) an extra restriction on $\Omega_M$ is necessary to improve
the constraint of the SNe Ia data on the parameters ($w_0$, $w_z$). A joint
analysis of SNe Ia data and BAO is made to break the degeneracy between $w$ and
$\Omega_M$, and leads to the interesting maximum likelihoods $w_0 = -0.94$ and
$w_z = 0$. When marginalizing the parameter $\Omega_M$, the fitting results are
found to be $(w_0, w_z)=(-0.95^{+0.45}_{-0.18}, 0.41^{+0.79}_{-0.96})$. After
adding the splitting angle statistic of SGL data, a consistent constraint is
obtained $(\Omega_M, w)=(0.298, -0.907)$ and the constraints on time-varying
dark energy are further improved to be $(w_0, w_z) = (-0.92^{+0.14}_{-0.10},
0.35^{+0.47}_{-0.54})$, which indicates that the phantom type models are
disfavored.
