Cosmological constraints on the new holographic dark energy model with action principle

Recently, a New HDE model with action principle was proposed (Li and Miao, arXiv:1210.0966). This model completely solves the causality and circular problems in the original HDE model, and is similar to the original model except a new term that can be interpreted as dark radiation. In this paper, we make further investigations on this model from the aspect of cosmological observations. Numerically, we confirm that the equations of motion force the $L(z=-1)=0$, making the cut-off $aL$ exactly the future event horizon. We also perform detailed analysis on the dynamical properties of the model, divided into the $c<6$ and $c\geq6$ cases ($c$ is a dimensionless parameter which should be decided by the data). From a combination of the present Union2.1+BAO+CMB+$H_0$ data, we find the model yields $\chi^2_{\rm min}=548.798$ (in a non-flat Universe), comparable to the results of the original HDE model (549.461) and the concordant $\Lambda$CDM model (550.354). At 95.4% CL, we get $1.41<c<3.09$ and correspondingly $-2.25<w(z=-1)<-1.39$, implying the Big Rip fate of the Universe at a high confidence level. Besides, for the constraints on dark radiation, we also get a rough estimation $N_{\rm \rm eff}=3.54^{+0.32+0.67}_{\rm -0.45-0.76}$, with the central value slightly larger than the standard value 3.046.