We perform a detailed investigation on the cosmological constraints on the holographic dark energy (HDE) model by using the Planck data. HDE can provide a good fit to Planck high-l (l>40) temperature power spectrum, while the discrepancy at l=20-40 found in LCDM remains unsolved in HDE. The Planck data alone can lead to strong and reliable constraint on the HDE parameter c. At 68% CL, we get c=0. 508+-0. 207 with Planck+WP+lensing, favoring the present phantom HDE at > 2sigma CL. Comparably, by using WMAP9 alone we cannot get interesting constraint on c. By combining Planck+WP with the BAO measurements from 6dFGS+SDSS DR7 (R) +BOSS DR9, the H0 measurement from HST, the SNLS3 and Union2. 1 SNIa data sets, we get 68% CL constraints c=0. 484+-0. 070, 0. 474+-0. 049, 0. 594+-0. 051 and 0. 642+-0. 066. Constraints can be improved by 2%-15% if we further add the Planck lensing data. Compared with the WMAP9 results, the Planck results reduce the error by 30%-60%, and prefer a phantom-like HDE at higher CL. We find no evident tension between Planck and BAO/HST. Especially, the strong correlation between Omegam h³ and dark energy parameters is helpful in relieving the tension between Planck and HST. The residual chi²₋₀₍₂₊+ₖ+₇ₒₓ-chi²₋₀₍₂₊+ₖ is 7. 8 in LCDM, and is reduced to 1. 0 or 0. 3 if we switch dark energy to the w model or the holographic model. We find SNLS3 is in tension with all other data sets; for Planck+WP, WMAP9 and BAO+HST, the corresponding Delta chi² is 6. 4, 3. 5 and 4. 1, respectively. Comparably, Union2. 1 is consistent with these data sets, but the combination Union2. 1+BAO+HST is in tension with Planck+WP+lensing, corresponding to a Delta chi² 8. 6 (1. 4% probability). Thus, it is not reasonable to perform an all-combined (CMB+SNIa+BAO+HST) analysis for HDE when using the Planck data. Our tightest self-consistent constraint is c=0. 495+-0. 039 obtained from Planck+WP+BAO+HST+lensing.
Li et al. (Wed,) studied this question.