| Dark energy turns out to be one of the most intriguing problems in modern cosmology. In this thesis, we study several projects related to unveiling the nature of dark energy.;As a negative pressure component, the most important property of dark energy is its equation of state w. We study the prospect of constraining w through a future weak-lensing survey by combining two methods: the tomographic shear-shear correlations and the number counts of the shear-selected galaxy clusters. We calculate the covariance between the two observables and find it negligible. By forecasting the constraining power through the Fisher matrix formalism, we find that each method has serious parameter degeneracy, hut their combination results in appreciable complementarity. In order to use the abundance of galaxy clusters to constrain dark energy, the primary systematic effect is uncertainty in the mass-observable scaling relations. For the X-ray clusters, we calibrate the preheating model for the intracluster gas by comparing its predictions for the X-ray Luminosity-Temperature relations with those of two cluster samples observed at different redshifts. We find that the required entropy level increases with time, which indicates the time-dependence of feedback on the intracluster gas cannot be discarded.;Instead of a missing unknown energy component, the dark energy problem may indicate that gravity deviates from GR on cosmological scales. We investigate the self-accelerating Dvali-Gabadadze-Porrati (DGP) model which explains the accelerated expansion of the universe from the perspective of modified gravity. By implementing the parameterized post-Friedmann (PPF) formalism into standard cosmological tools, we can calculate the growth of structure in DGP efficiently. This allows us to perform a thorough Markov Chain Monte Carlo analysis of the model, given the current observations of the anisotropies of the cosmic microwave background, magnitude of the supernovae and the Hubble constant. Our results show that this model cannot fit both the geometry and growth data simultaneously, with its best-fit nominally 5sigma poorer than that of the concordance ACDM model.;If dark energy is not a cosmological constant, it clusters in space. The clustering properties are well described for the scalar field dark energy models. However, if w evolves across the phantom divide defined by w = -1, to avoid instabilities in the perturbations, the dark energy cannot be realized by a single scalar field, but a composite of multiple fields, the construction of which is cumbersome. We introduce a PPF description for these smooth dark energy models to avoid this difficulty. By comparing with true scalar field models, we find that the PPF description gives accurate results. |
