Advances in High Energy Physics

Volume 2015 (2015), Article ID 952156, 10 pages

http://dx.doi.org/10.1155/2015/952156

## Cosmological Evolution of Pilgrim Dark Energy in Gravity

Department of Mathematics, COMSATS Institute of Information Technology, Lahore 54000, Pakistan

Received 4 January 2015; Revised 21 February 2015; Accepted 1 March 2015

Academic Editor: Elias C. Vagenas

Copyright © 2015 Abdul Jawad and Shamaila Rani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

We analyze the behavior of pilgrim dark energy with Hubble horizon in gravity. We reconstruct the models through correspondence phenomenon by assuming two values of pilgrim dark energy parameter . We evaluate the equation of state parameter which shows evolution of the universe in the quintessence, vacuum, and phantom phase for both cases of and give favor the pilgrim dark energy phenomenon. Also, squared speed of sound exhibits the stability of model for both cases of . The also provides freezing and thawing regions in this scenario. In this framework, the plane also corresponds to different dark energy scenarios.

#### 1. Introduction

It is confirmed through different observational schemes that our universe undergoes accelerated expansion. The pioneer observations about this accelerated expansion phenomenon was made by a variety of astronomers through supernova type Ia [1, 2]. The subsequent attempts in this regard also favor this phenomenon [3–6]. The background force which acts upon behind this phenomenon is an exotic type called dark energy (DE) whose nature is still under consideration. In order to understand its nature, various approaches have been adopted, the proposal of different dynamical DE models [7–14] and modified theories of gravity [15–19] to peruse the DE problem.

Moreover, the accelerated expansion is also discussed widely in the literature through correspondence phenomenon of dynamical DE models with modified gravity. Many works have been done in this direction by adopting different scenarios in modified gravity theories [20–25]. Further, Setare and Saridakis [26] considered the holographic and Gauss-Bonnet DE models separately to investigate the conditions under which these models can be simultaneously valid. They found that this correspondence phenomenon leads to accelerated expansion of the universe. Also, they investigated the correspondence of HDE model with canonical, phantom, and quintom models minimally coupled to gravity and pointed out consistent results about acceleration of the universe [27]. Further, Setare [28–32] has studied this correspondence scenario incorporating different dynamical DE models as well as modified theories of gravity in this respect. We have also investigated the correspondence phenomenon of various DE models with modified gravities and found that these scenarios favor the accelerated expansion phenomenon of the universe [33–39].

The bound of energy density as suggested by Cohen et al. [40] predicts the formation of black hole (BH) in quantum gravity. However, it is suggested that formation of BH can be avoided through appropriate repulsive force which resists the matter collapse phenomenon. This force can only provide phantom DE in spite of other phases of DE like vacuum and quintessence DE. By keeping in mind this phenomenon, Wei [41] has suggested the DE model called pilgrim DE (PDE) on the speculation in which phantom DE possesses the large negative pressure as compared to the quintessence DE which helps in violating the null energy condition and possibly prevent the formation of BH. In the past, many applications of phantom DE exist in the literature. For instance, phantom DE also plays an important role on the reduction of masses of BHs [42–45] and in the wormhole physics where the event horizon can be avoided due to its presence [46–50].

In the present work, we present the reconstruction scenario of newly proposed DE model called pilgrim DE (PDE) with the gravity. We will construct models and analyze it through different cosmological parameters as well as cosmological planes. The paper is organized as follows: next section contains the discussion of models. In Section 3, we provide the analysis of EoS parameter, squared speed of sound, -, and - planes. The last section contains the summary of the outcomes.

#### 2. Pilgrim Dark Energy Models

It was demonstrated by Sahni and Starobinsky [51] that there is also a possibility to write the field equations in modified gravities in terms of usual Einstein field equations by transferring all additional terms from the left-hand side into the right-hand side of the Einstein equations and called them as an effective energy momentum tensor of DE. Here, we consider gravity where the modified field equations are [51, 52]The subscripts indicate the matter contribution of energy density and pressure and is the Hubble parameter with dot representing the time derivative. The Gauss-Bonnet invariant for FRW metric becomes . Also,Here, we will incorporate with the pressureless matter, that is, , while the energy density of matter satisfies the following energy conservation equation:This equation has a solution which is given by the following expression:where is an arbitrary constant.

It is predicted that phantom DE with strong negative pressure can push the universe towards the big rip singularity where all the physical objects lose the gravitational bounds and finally dispersed. This prediction supports the phenomenon of the avoidance of BH formation and motivated Wei [41] in constructing PDE model. The PDE model is defined aswhere is the IR cutoff and size of the system, is the PDE parameter, is conventional constant, and is reduced Planck mass. Wei analyzed the PDE model through different possible theoretical and observational ways to make the BH-free phantom universe with Hubble horizon () through PDE parameter (). Further, Sharif and Jawad [43–45] have analyzed this proposal in detail by choosing different IR cutoffs through well-known cosmological parameters in flat and nonflat universes. This model has also been in different modified gravities [53, 54].

Here, we make correspondence between PDE and model by equating their energy densities; that is, . It yieldsTo find out an analytic solution of (6), we assume a power-law form of the scale factor as follows:where the constant represents the present day value of the scale factor. By using (7) in the reconstructed equation, we obtainEquation (8) is a second-order linear differential equation whose solution is given bywhere and are integration constants andEquation (9) represents the reconstructed PDE model which we have plotted for three different values of 2, 2.2, and 2.4 as shown in Figures 1 and 2. The assumptions of other constants parameters are . Figure 1 shows that the model versus exhibits decreasing behavior initially and then approaches after some interval. After that, it shows increasing behavior forever for all values of . Figure 2 represents that the reconstructed function shows rapid decrease initially and then approaches positive value forever for all values of .