Holographic Dark Energy In Brans-Dicke Theory

Recent astronomical observations suggest that the universe is spatially flat and undergoing a period of accelerated expansion. To explain the cosmic acceleration, an exotic energy component, called'dark energy', is introduced. The observational data, from Wilkinson Microwave Anisotropy Probe (WMAP) , strongly implies that dark energy contributes to 76 % of the total energy of the universe, dark matter contributes to 20%, and normal matter contributes to only about 4%. Therefore, the universe is dominated by dark energy now. This result is a big challenge to Einstein's general relativity which believes that gravity slows down the expansion of the universe. Unfortunately, we know nothing about dark energy. Therefore, the research about dark energy still remains one of the most significant, and hot fields in modern cosmology.In this dissertation,a brief introduction to dark energy was given. Firstly, in view of the astronomical observations, we use the observational data to analyze the Chevallier-Polarski-Linder (CPL)and Jassal-Bagla-Padmanabhan (JBP) models, and reconstruct the equation of state of dark energy parameter w( z ). We also study the constraints on the dark energy model with constant equation of state and the holographic dark energy (HDE) model by using the weak gravity conjecture. The combination of weak gravity conjecture and the observational data give w < ?0 .7 at the 3σconfidence level. The HDE model realized by a scalar field is in swampland. Besides, for theoretical models, we focus on the HDE model in the fromework of Brans- Dicke theory as well as the holographic dark energy model, and study the extended holographic dark energy (EHDE) model in detail. Many studies show that, both HDE and EHDE, would come into the plight of theoretical loop, if the infrared cut-off relevant to the dark energy is the size of the event horizon. However, if the IR cut-off is the Hubble horizon, then the theoretical problem would be solved which is the key point in our research.The research about dark energy is just begining, although almost all theoretical models are not convincing, it provides an opportunity to the birth of a new underlying theory. What we have done offers a new perspcetive, and much more work remains to be done.