Correspondence off(R,∇R)Modified Gravity with Scalar Field Models

Abdul Jawad,Ujjal Debnath

doi:10.1155/2014/594781

Abstract

This paper is devoted to study the scalar field dark energy models by taking its different aspects in the framework off(R,∇R)gravity. We consider flat FRW universe to construct the equation of state parameter governed byf(R,∇R)gravity. The stability of the model is discussed with the help of squared speed of sound parameter. It is found that models show quintessence behavior of the universe in stable as well as unstable modes. We also develop the correspondence off(R,∇R)model with some scalar field dark energy models like quintessence, tachyonic field,k-essence, dilaton, hessence, and DBI-essence. The nature of scalar fields and corresponding scalar potentials is being analyzed inf(R,∇R)gravity graphically which show consistency with the present day observations about accelerated phenomenon.

Highlights

It is strongly believed that the universe is experiencing an accelerated expansion nowadays
The most appealing and simplest candidate for dark energy” (DE) is the cosmological constant Λ [6,7,8] which has the equation of state (EoS) parameter ω = −1
A positive value indicates the stability of model whereas instability stands for the negative value of Vs2

Summary

Introduction

It is strongly believed that the universe is experiencing an accelerated expansion nowadays. The quintessence scalar field model has been proposed to resolve the fine-tuning problem taking EoS as time dependent instead of constant This model can explain current cosmic acceleration by giving negative pressure when potential dominates the kinetic term. The evolution trajectories of scalar field and potential function versus time for f(R, ∇R) quintessence model are shown in Figure 2 taking the same values of constants as for effective EoS parameter. The scalar field represents increasing behavior versus time and indicates more steeper behavior for n = 1 This leads to the decreasing kinetic energy, approximately zero value. The quintessence scalar field relies on potential energy in order to explain late time cosmic acceleration of the universe This model takes the modifications of kinetic energy in the scalar fields to address the cosmic expansion.

The corresponding EoS parameter yields ωK

The EoS parameter takes the form ωD

Concluding Remarks