We investigate the observational signatures of the holographic dark energy models in this paper , including both the original model and a model with an interaction term between the dark energy and dark matter .
We first delineate the dynamical behavior of such models , especially whether they would have “ Big Rip ” for different parameters , then we use several recent observations , including 182 high-quality type Ia supernovae data observed with the Hubble Space Telescope , the SNLS and ESSENCE surveys , 42 latest Chandra X-ray cluster gas mass fraction , 27 high-redshift gamma-ray burst samples , the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey , and the CMB shift parameter from WMAP three years result to give more reliable and tighter constraints on the holographic dark energy models .
The results of our constraints for the holographic dark energy model without interaction is c = 0.748 ^ { +0.108 } _ { -0.009 } , \Omega _ { \mathrm { m 0 } } = 0.276 ^ { +0.017 } _ { -0.016 } , and for model with interaction ( c = 0.692 ^ { +0.135 } _ { -0.107 } , \Omega _ { \mathrm { m 0 } } = 0.281 ^ { +0.017 } _ { -0.017 } , \alpha = -0.006 ^ { +0.021 } _ { -0.024 } , where \alpha is an interacting parameter ) .
As these models have more parameters than the \Lambda CDM model , we use the Bayesian evidence as a model selection criterion to make comparison .
We found that the holographic dark energy models are mildly favored by the observations compared with the \mathrm { \Lambda CDM } model .