The dynamics of interacting dark energy model in loop quantum cosmology (LQC) is studied in this paper. The dark energy has a constant equation of state $w_x$ and interacts with dark matter through a form $3cH(rho_x+rho_m)$. We find for quintessence
model ($w_x>-1$) the cosmological evolution in LQC is the same as that in classical Einstein cosmology; whereas for phantom dark energy ($w_x<-1$), although there are the same critical points in LQC and classical Einstein cosmology, loop quantum effect reduces significantly the parameter spacetime ($c, w_x$) required by stability. If parameters $c$ and $w_x$ satisfy the conditions that the critical points are existent and stable, the universe will enter an era dominated by dark energy and dark matter with a constant energy ratio between them, and accelerate forever; otherwise it will enter an oscillatory regime. Comparing our results with the observations we find at $1sigma$ confidence level the universe will accelerate forever.
With a model independent method the expansion history $H(z)$, the deceleration parameter $q(z)$ of the universe and the equation of state $w(z)$ for the dark energy are reconstructed directly from the 192 Sne Ia data points, which contain the new ESS
ENCE Sne Ia data and the high redshift Sne Ia data. We find that the evolving properties of $q(z)$ and $w(z)$ reconstructed from the 192 Sne Ia data seem to be weaker than that obtained from the Gold set, but stronger than that from the SNLS set. With a combination of the 192 Sne Ia and BAO data, a tight constraint on $Omega_{m0}$ is obtained. At the $1sigma$ confidence level $Omega_{m0}=0.278^{+0.024}_{-0.023}$, which is highly consistent with that from the Gold+BAO and SNLS+BAO.
We explore the properties of dark energy from recent observational data, including the Gold Sne Ia, the baryonic acoustic oscillation peak from SDSS, the CMB shift parameter from WMAP3, the X-ray gas mass fraction in cluster and the Hubble parameter
versus redshift. The $Lambda CDM$ model with curvature and two parameterized dark energy models are studied. For the $Lambda CDM$ model, we find that the flat universe is consistent with observations at the $1sigma$ confidence level and a closed universe is slightly favored by these data. For two parameterized dark energy models, with the prior given on the present matter density, $Omega_{m0}$, with $Omega_{m0}=0.24$, $Omega_{m0}=0.28$ and $Omega_{m0}=0.32$, our result seems to suggest that the trend of $Omega_{m0}$ dependence for an evolving dark energy from a combination of the observational data sets is model-dependent.
