Planck constraints on holographic dark energy

We perform a detailed investigation on the cosmological constraints on the holographic dark energy (HDE) model by using the Planck data. We find that HDE can provide a good fit to the Planck high-l (l greater than or similar to 40) temperature power spectrum, while the discrepancy at 20 40 found in the ACDM model remains unsolved in the HDE model. The Planck 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 Planck+WP-lensing, favoring the present phantom behavior of HDE at the more than 2 sigma CL. By combining Planck+WP with the external astrophysical data sets, i.e. the BAO measurements from 6dFGS-FSDSS DR7(R)+BOSS DR9, the direct Hubble constant measurement result (Ho = 73.8 +/- 2.4 km s(-1) Mpc(-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 Planck lensing data into the analysis. Compared with the WMAP-9 results, the Planck 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 Planck data with BAO and HST. Especially, we find that the strong correlation between Omega(m)h(3) and dark energy parameters is helpful in relieving the tension between the Planck and HST measurements. The residual value of chi(2)Planck+WP+HST (-) chi(2)Planck+WP is 7.8 in the ACDM 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 Planck+WP, WMAP-9 and BAO+HST, the corresponding Delta chi(2) 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 Pianck+WP-Flensing, corresponding to a large Delta chi(2) that is equal to 8.6 (1.4% probability). Thus, combining internal inconsistent data sets (SNIa+BAO+HST with Planck+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 Planck+WP+BAO-FHST-Flensing.