Phantom and Quintessence Fields Coupled to Scalar Curvature in General &amp;lt;i&amp;gt;f(R)&amp;lt;/i&amp;gt; Gravity Theory

Xinyou Zhang,Yongchang Huang

doi:10.4236/jmp.2017.88081

Abstract

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.

Highlights

Researchers began to question the theory of gravity after the advent of the theory of general relativity (GR)
We present a new general action of f(R) gravity and Phantom and Quintessence fields coupled to scalar curvature
We generalize Equation (4) to a general action of f ( R) gravity and Phantom and Quintessence fields coupled to scalar curvature by making variance of the general Lagrangian

Summary

Introduction

Researchers began to question the theory of gravity after the advent of the theory of general relativity (GR). 2. General Action of f(R) Gravity and Phantom and Quintessence Fields Coupled to the Scalar Curvature. Equation (5) is a new action with f ( R) gravity, Phantom and Quintessence fields and scalar curvature R. We generalize Equation (4) to a general action of f ( R) gravity and Phantom and Quintessence fields coupled to scalar curvature by making variance of the general Lagrangian. 3. Exact Energy-Momentum Tensor and Sound Speed of the New General Single Field Action of f(R) Gravity. We obtain the general energy-momentum tensor, pressure, density and speed sound of the new general single field action of f ( R) gravity and Phantom and Quintessence fields coupled to scalar curvature

Different Cosmological Evolutions with Single Field Inflation

Findings

Summary and Conclusions