Exploring plane-symmetric solutions in f ( R ) gravity
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LECTRONIC PROPERTIES OF SOLID
Exploring Plane-Symmetric Solutions in f(R) Gravity1 M. F. Shamir* Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Pakistan *e-mail: [email protected] Received May 4, 2015
Abstract—The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane-symmetric solutions in the context of metric f(R) gravity. We extend the work on static plane-symmetric vacuum solutions in f(R) gravity already available in the literature [1, 2]. The modified field equations are solved using the assumptions of both constant and nonconstant scalar curvature. Some well-known solutions are recovered with power-law and logarithmic forms of f(R) models. DOI: 10.1134/S106377611601009X
1. INTRODUCTION Astrophysical data coming from different sources, such as Cosmic Microwave Background fluctuations [3], supernovae type-Ia experiments [4], X-ray experiments [5], and large-scale structure [6] have revealed a completely different picture of our universe. All these observations suggest that the universe is expanding with an accelerating rate. The phenomenon of dark energy and dark matter is another topic of discussion [7]. It was Einstein who first gave the concept of dark energy and introduced the small positive cosmological constant in the field equations. But after sometime he referred to it as the biggest mistake in his life. However, it is now believed that our universe is filled with an exotic cosmic fluid known as dark energy, with strong negative pressure, and the cosmological constant may be a suitable candidate for dark energy. There exist two basic models for dark energy. In the first model, it is associated with empty space and remains constant throughout the space-time, suggesting the need of the cosmological constant in the field equations. The second model proposes that it varies over the space-time and cosmic expansion is achieved by a scalar field. Different models have been proposed involving a scalar field, i.e., quintessence [8], k-essence [9], Chaplygin gas [10], and phantom models [11]. It has been predicted that 96% of energy of the universe is either dark energy or dark matter (76% dark energy and 20% dark matter) [7]. Matter and energy domination seems to be a justified reason for this accelerating phase. We can describe dark energy with an equation of state (EOS) parameter ω = p/ρ, where ρ and p represent the energy 1The article is published in the original.
density and pressure of dark energy. It has been established that the expansion of the universe is accelerating when ω ≈ –1 [12]. The universe is found to have a quintessence dark era when ω > –1, while the phantom-like dark energy exists in the region where ω < ‒1. The universe with phantom-like dark energy ends up with a finite time future singularity known as the Big Rip or cosmic doomsday [13]. Some other observations like rotational velocities of galaxies, the temperature distrib
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