Latest Cosmological Constraints on Cardassian expansion models including the updated Gamma-ray bursts

In this paper, we constrain the Cardassian expansion models from the latest observations including the updated Gamma-ray bursts (GRBs), which calibrated cosmology-independently from the Union2 compilation of type Ia supernovae (SNe Ia). By combining the GRB data to the joint observations with the Union2 SNe Ia set, along with the Cosmic Microwave Background radiation observation from the seven-year Wilkinson Microwave Anisotropy Probe result, the baryonic acoustic oscillation observation from the spectroscopic Sloan Digital Sky Survey Data Release galaxy sample, we find significant constraints on model parameters of the original Cardassian model $\Omega_{{\rm M0}}=0.282_{-0.014}^{+0.015}$, $n= 0.03_{-0.05}^{+0.05}$; and $n= -0.16_{-3.26}^{+0.25}$, $\beta=0.76_{-0.58}^{+0.34}$ of the modified polytropic Cardassian model, which are consistent with the $\Lambda$CDM model in 1-$\sigma$ confidence region. From the reconstruction of the deceleration parameter $q(z)$ in Cardassian models, we obtain the transition redshift $z_{\rm T}=0.73\pm{0.04}$ for the original Cardassian model, and $z_{\rm\rm T}=0.68\pm{0.04}$ for the modified polytropic Cardassian model.