Emergence Of Space And The Thermodynamic Description On The Event Horizon In The FRW Universe

From decades of research results, we may come to a conclusion that space-time is composed of microscopic degrees of freedom. We know that macroscopic objects are composed of microscopic degrees of freedom and the expression of the laws of thermodynamics can be derived by using quantum statistical methods. Based on the same reason, if spacetime is composed of microscopic degrees of freedom, then we believe we can also set up a statistical theory to quantize grav-ity. This is a possible way of quantum gravity. So it is very meaningful to study the thermodynamic description of gravitation. In this thesis, we mainly study the evolution of the FRW universe in different models and the first law of thermody-namics on the event horizon of the FRW universe. Furthermore, we discuss the important relationships between microscopic degrees of freedom of spacetime and gravitational dynamics, and between thermodynamics of horizon and gravitation-al dynamics. We propose that the number of degrees of freedom on the horizon should be expressed in terms of entropy, rather than the horizon area divided by the Planck area. Then we explore the dynamical evolution equation of the FRW universe in f(R) gravity and deformed Horava-Lifshitz gravity from the perspec-tive that space is emergent as time progresses (For short, emergence of space). Under such a perspective, a cosmological constant is usually introduced in order to obtain the results of the accelerated expansion of the universe. However, we propose that the accelerated expansion of the universe is caused by the surface term (the effects of the entropic force) rather than by the cosmological constant because there exists an important relation between the surface term and the bulk tern in Einstein-Hilbert action. Based on such a proposal, we study the expansion of the FRW universe and obtain some good results. Finally, we investigate the thermodynamic description on the cosmological event horizon. We show that the equivalency between the first law of thermodynamics and the dynamic equations of the FRW universe with any spatial curvature by redefining a temperature on the event horizon in Einstein gravity and f(R) gravity. We also investigate the generalized second law of thermodynamics of the universe bounded by the event horizon in Einstein gravity and f(R) gravity.