We review the problem of dark energy, including a survey of theoretical models and some aspects of numerical studies.

We review the paradigm of holographic dark energy (HDE), which arises from a theoretical attempt of applying the holographic principle (HP) to the dark energy (DE) problem. Making use of the HP and the dimensional analysis, we derive the general formula of the energy density of HDE. Then, we describe the properties of HDE model, in which the future event horizon is chosen as the characteristic length scale. We also introduce the theoretical explorations and the observational constraints for this model. Next, in the framework of HDE, we discuss various topics, such as spatial curvature, neutrino, instability of perturbation, time-varying gravitational constant, inflation, black hole and big rip singularity. In addition, from both the theoretical and the observational aspects, we introduce the interacting holographic dark energy scenario, where the interaction between dark matter and HDE is taken into account. Furthermore, we discuss the HDE scenario in various modified gravity (MG) theories, such as Brans-Dicke theory, braneworld theory, scalar-tensor theory, Horava-Lifshitz theory, and so on. Besides, we introduce the attempts of reconstructing various scalar-field DE and MG models from HDE. Moreover, we introduce other DE models inspired by the HP, in which different characteristic length scales are chosen. Finally, we make comparisons among various HP-inspired DE models, by using cosmological observations and diagnostic tools.

The holographic principle of quantum gravity theory has been applied to the dark energy (DE) problem, and so far three holographic DE models have been proposed: the original holographic dark energy (HDE) model, the agegraphic dark energy (ADE) model, and the holographic Ricci dark energy (RDE) model. In this work, we perform the best-fit analysis on these three models, by using the latest observational data including the Union+CFA3 sample of 397 Type Ia supernovae (SNIa), the shift parameter of the cosmic microwave background (CMB) given by the five-year Wilkinson Microwave Anisotropy Probe (WMAP5) observations, and the baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS). The analysis shows that for HDE, χ 2 min = 465.912; for RDE, χ 2 min = 483.130; for ADE, χ 2 min = 481.694. Among these models, HDE model can give the smallest χ 2 min . Besides, we also use the Bayesian evidence (BE) as a model selection criterion to make a comparison. It is found that for HDE, ADE, and RDE, ∆ ln BE = −0.86, −5.17, and −8.14, respectively. So, it seems that the HDE model is more favored by the observational data. PACS numbers: 98.80.-k, 95.36.+x I. INTRODUCTION Observations of Type Ia supernovae (SNIa) [1], cosmic microwave background (CMB) [2] and large scale structure (LSS) [3] all indicate the existence of mysterious dark energy (DE) driving the current accelerating expansion of the universe. The most obvious theoretical candidate of dark energy is the cosmological * Electronic address: mli@itp.ac.cn † Electronic address:

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