Abstract
We perform a detailed investigation on the cosmological constraints on the holographic dark energy (HDE) model by using the Plank data. We find that HDE can provide a good fit to the Plank high-ℓ (ℓ ≳ 40) temperature power spectrum, while the discrepancy at ℓ ≃ 20-40 found in the ΛCDM model remains unsolved in the HDE model. The Plank data alone can lead to strong and reliable constraint on the HDE parameter c. At the 68% confidence level (CL), we obtain c = 0.508 ± 0.207 with Plank+WP+lensing, favoring the present phantom behavior of HDE at the more than 2σ CL. By combining Plank+WP with the external astrophysical data sets, i.e. the BAO measurements from 6dFGS+SDSS DR7(R)+BOSS DR9, the direct Hubble constant measurement result (H0 = 73.8 ± 2.4 kms−1Mpc−1) from the HST, the SNLS3 supernovae data set, and Union2.1 supernovae data set, we get the 68% CL constraint results c = 0.484 ± 0.070, 0.474 ± 0.049, 0.594 ± 0.051, and 0.642 ± 0.066, respectively. The constraints can be improved by 2%-15% if we further add the Plank lensing data into the analysis. Compared with the WMAP-9 results, the Plank results reduce the error by 30%-60%, and prefer a phantom-like HDE at higher significant level. We also investigate the tension between different data sets. We find no evident tension when we combine Plank data with BAO and HST. Especially, we find that the strong correlation between Ωmh3 and dark energy parameters is helpful in relieving the tension between the Plank and HST measurements. The residual value of χ2Plank+WP+HST−χ2Plank+WP is 7.8 in the ΛCDM model, and is reduced to 1.0 or 0.3 if we switch the dark energy to w model or the holographic model. When we introduce supernovae data sets into the analysis, some tension appears. We find that the SNLS3 data set is in tension with all other data sets; for example, for the Plank+WP, WMAP-9 and BAO+HST, the corresponding Δχ2 is equal to 6.4, 3.5 and 4.1, respectively. As a comparison, the Union2.1 data set is consistent with these three data sets, but the combination Union2.1+BAO+HST is in tension with Plank+WP+lensing, corresponding to a large Δχ2 that is equal to 8.6 (1.4% probability). Thus, combining internal inconsistent data sets (SNIa+BAO+HST with Plank+WP+lensing) can lead to ambiguous results, and it is necessary to perform the HDE data analysis for each independent data sets. Our tightest self-consistent constraint is c = 0.495 ± 0.039 obtained from Plank+WP+BAO+HST+lensing.