the measurement data [@sdssred] $A_0=0.469\pm 0.017$. We also include the LSS constraint in our analysis by adding $\chi_{\rm
LSS}^2=[(A-A_0)/\sigma_A]^2$ (see e.g. Refs. [@holoSN; @gyg]), where $A$ is computed by the NGCG model using equation (\[A\]). Note that we have chosen to use only the most conservative and robust information, ${\cal R}$ and $A$, from CMB and LSS observations. These measurements we use do not depend on the Hubble constant $H_0$, thus are useful complements to the SNe data. It is remarkable that the likelihood analysis scheme we employ here is very economical and efficient due to that it does not make use of all the information available in CMB and LSS but can provide fairly good constraints on dark energy models [@holoSN; @gyg].

We now analyze the probability distribution of $\eta$ and $w_X$ in the NGCG model. The likelihood of these two parameters is determined by minimizing over the “nuisance” parameters $${\cal L}(\eta,w_X)=\int dhd\Omega_{dm}^0~ e^{-\chi^2/2}~,$$ where the integral is over a large enough range of $h$ and $\Omega_{dm}^0$ to include almost all the probability. We now compute ${\cal L}(\eta,w_X)$ on a two-dimensional grid spanned by $\eta$ and $w_X$. The $68.3\%$, $95.4\%$, and $99.7\%$ (namely 1, 2, and 3 $\sigma$) confidence 