Theoretical Research On Holographic Gravity And Holographic Dark Energy

We study the holographic principle in several fields of research. Firstly, we investigate the theory of entropic gravity. We derive Einstein equations from the first law of thermodynamics and the conservation of energy flow on the holo-graphic screen, respectively. Our approaches show more details than Verlinde’s and Jacobson’s approaches. We prove that Einstein equations are the integra-bility conditions of the first law of thermodynamics on the boundary. Besides, our results show that the minimal change of black hole entropy is quantized in the quasi-static process. Secondly, we investigate the holographic dark energy. We discuss the possible origin of holographic dark energy as Casimir energy, and we solve the causality problem and circular logic problem in the model of holo-graphic dark energy. What is more, we propose a new model of holographic dark energy. Interestingly, this new model is very similar to the initial one of Li except a new term which may be explained as dark radiation. Thirdly, we investigate the holographic Weyl Anomaly and entanglement entropy. We develop a general approach to simplify the derivation of the holographic Weyl anomaly. We only need to calculate a few relevant terms in our approach. Interestingly, to derive all the central charges of4d and6d CFTs, we make no use of equations of motion. Applying our method and Dong’s proposal of holographic entanglement entropy, we derive the correct universal term of entanglement entropy for4d CFTs. This is a nontrivial test of Dong’s proposal. Fourthly, we investigate the theory of f(T) gravity. We find that there are five degrees of freedom in f(T) gravity. Besides, we prove that the first law of thermodynamics is violated due to the lack of local Lorentz invariance in f(T) gravity.