Theoretical Research On Cosmology And Compact Objects

In this dissertation, we study the models of dark energy based on the observational data and the properties of the highly dense astronomic objects, including the observational signals, the thermodynamics and phase transitions of black holes, slowly rotating strange star.To explain the recent observational data of the suppression of the CMB power spectrum at small l, we employ the holographic cosmic duality to study the cosmology. We obtain a reasonable agreement between the holographic predictions of CMB at small l and the WMAP observation, showing the power of the holographic idea. We also use this idea to constrain some models of dark energy and their evolutions.We have established a model on the modern accelerating universe, inspired by the Dirac's Large Number Hypothesis. This model can unify the Einstein general relativity and Dirac cosmology. After adjusting the model parameters by using the supernova data, we calculate a series of cosmological quantities. Our results agree the recent observation data well and suggest that 1) " the gravitational constant" is not a constant on the cosmological scale and actually is decreasing by time; 2) the addition creation and multiplication creation in Dirac cosmology are the dark energy and dark matter respectively. We have shown that our theory is consistent with the solar system tests.In order to verify the existence of the extra dimensions in the experiments, we study the Quasi-Normal Modes (QNM) and the Hawking radiation for both scalar and brane-localized gravitational perturbations in the background of a brane-world black hole with a tidal charge. Comparing with four-dimensional black holes, we have observed that the signature of the tidal charge can present the effects of the extra dimensions both in the QNM and the Hawking radiation. Our results provide theoretical investigations on the existence of the extra dimensions for the future experimental observations.We also reexamined the argument that the QNM could be a probe of the phase transition of black hole. We investigate the behavior of QNM near the critical point of the black hole phase transition between a topological black hole and a hairy black hole. We find the evidence that QNM can reflect this phase transition. Further, we calculate the QNM near the critical point of phase transition between a flat AdS black hole and an AdS soliton spacetime, in order to understand the relation between black hole phase transition and QNM. But we do not find any dramatic changes at the critical point. Therefore, the original argument should be investigated in subtler studies.To understand black hole's phase transition and its thermodynamics, we introduce Ruppeiner's thermodynamic geometry into the thermodynamics of black hole. Based on the analogy between the RN-AdS black holes and the van der Waals-Maxwell liquid-gas system, we study the Ruppeiner geometry whose metrics are the functions with respect to the internal energy of black hole and electric potential(angular velocity), for RN, Kerr and RN-AdS black holes. Our results are in good agreement of the Davies' phase transition. We also study the critical behavior with the Ruppeiner geometry.In the study of strange star, we employ the equation of state of strange matter induced by the Quark Mass Density- and Temperature- Dependent model and Hartle's method to configure hot and slowly rotating strange star. We investigate the star's mass-radius relation, the moment of inertia and the frame dragging and find some important influences of temperature and rotating frequency on the configuration of star. We also extend the Hartle's method to the differential rotating star.