Reconstruction Of Dark Energy And Generalized F(R) Gravity

A large number of observations indicate that our universe is in period of the accelerating expansion. In order to explain the accelerating expansion of the universe, there are two research approaches on the international:One is to modify the right side of Einstein’s equation, intro-ducing an exotic component with large negative pressure, usually referred to as dark energy; The other is to modify the left side of Einstein’s equation, which is the part of geometry, called modified theories of gravity. The nature of dark energy is still unknown, so many theoretical models have been suggested to describe its behavior:For example, the cosmological constant, the scalar field dark energy models, Chaplygin gas, the holographic dark energy model, the new Agegraphic dark energy and the holographic Ricci dark energy and so on. The modified theo-ries of gravity include f(R), f(T), f(G), etc. f(R) theories of gravity is the most widely studied by people in them. Both the dark energy theories and the modified theories of gravity can explain the accelerated expansion of the universe, which inspires us to use this feature to construct the specific models of f(R) according to the modern astronomical observations.In this paper we will select the holographic dark energy model, new Agegraphic dark en-ergy model and the holographic Ricci dark energy model to construct the different modified gravity f(R) models. Research results include non-coupling, non-minimal coupling and arbi-trary coupling as special cases.