Author(s)

Xinyou Zhang^1,2*, Yongchang Huang^2,3,4

¹Group of Mathematics and Physics, Jiangxi University of TCM, Nanchang, China.
²Institute of Theoretical Physics, Beijing University of Technology, Beijing, China.
³Kavli Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.
⁴CCAST (WorldLab.), Beijing, China.

This paper reviews the development of f(R) gravity theory and Phantom and Quintessence fields. Specifically, we present a new general action of f(R) gravity and Phantom and Quintessence fields coupled to scalar curvature. Then, we deduce Euler-Lagrange Equations of different fields, matter tensor and effective matter tensor. Additionally, this paper obtains the general pressure, density and speed sound of the new general field action, and investigates different cosmological evolutions with inflation. Further, this paper investigates a general f(R) gravity theory with a general matter action and obtains the different field equations, general matter tensor and effective matter tensor. Besides, this paper obtains the effective Strong Energy Condition (SEC) and effective Null Energy Condition (NEC). Then, we prove that when f(R) approaches to R, the effective SEC and the effective NEC approach to the usual SEC and the usual NEC, respectively. Finally, this paper presents a general action of f(R) gravity, Quintessence and Phantom fields and their applications.

Theory of f(R) Gravity, Dark Energy, Sound Speed, Quintessence Field, Phantom Field