Miao Li

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 h^3 and dark energy parameters is helpful in relieving the tension between Planck and HST. The residual chi^2_{Planck+WP+HST}-chi^2_{Planck+WP} 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 chi^2 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 chi^2 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.

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.

The problem of dark energy is briefly reviewed in both theoretical and observational aspects. In the theoretical aspect, dark energy scenarios are classified into symmetry, anthropic principle, tuning mechanism, modified gravity, quantum cosmology, holographic principle, back-reaction and phenomenological types. In the observational aspect, we introduce cosmic probes, dark energy related projects, observational constraints on theoretical models and model independent reconstructions.

We propose a new model of holographic dark energy with an action. It is the first time that one can derive a HDE model from the action principle. The puzzles of causality and circular logic about HDE have been completely solved in this model. The evolution of the universe only depends on the present state of the universe, clearly showing that it obeys the law of causality. Furthermore, the use of future event horizon as a present cut-off is not an input but automatically follows from equations of motion. Interestingly, this new model is very similar to the initial one of Li except a new term which may be explained as dark radiation.