is linear, $r_0=1+{9\over
2}w_X\Omega_X^0 s_0$.

Observational constraints from SNe Ia, CMB, and LSS data
========================================================

In this section we will derive the constraints on the NGCG model from current available observational data. It should be mentioned that the interacting XCDM parametrization scenario has been tested by the recent Type Ia supernovae data [@IXCDM]. The results show that the SNe Ia data favor a negative coupling and an equation of state $w_X<-1$, namely a negatively coupled phantom dark energy. However, as we know, the supernovae data alone are not sufficient to constrain dark energy models strictly (see e.g. the analysis in Ref. [@holoSN]). Therefore, to obtain more tight constraints on dark energy models, one should need additional data provided by other astronomical observations to be necessary and useful complements to the SNe data. It has been demonstrated that some observational quantities irrelevant to $H_0$ are very suitable to play this role [@wangyun]. Such quantities and data can be found in the probes of CMB and LSS [@holoSN; @wangyun; @Xia; @starob; @gyg]. In what follows we perform a combined analysis of SNe Ia, CMB, and LSS on the constraints of the NGCG model. We use a $\chi^2$ statistic $$\chi^2=\chi_{\rm SN}^2+\chi_{\rm CMB}^2+\chi_{\rm LSS}^2~,$$ 