Energy conditions in \(f(\mathcal {G},T)\) gravity

The European Physical Journal C, Nov 2016

The aim of this paper is to introduce a new modified gravity theory named \(f(\mathcal {G},T)\) gravity (\(\mathcal {G}\) and T are the Gauss–Bonnet invariant and trace of the energy-momentum tensor, respectively) and investigate energy conditions for two reconstructed models in the context of FRW universe. We formulate general field equations, divergence of energy-momentum tensor, equation of motion for test particles as well as corresponding energy conditions. The massive test particles follow non-geodesic lines of geometry due to the presence of an extra force. We express the energy conditions in terms of cosmological parameters like the deceleration, jerk, and snap parameters. The reconstruction technique is applied to this theory using de Sitter and power-law cosmological solutions. We analyze the energy bounds and obtain feasible constraints on the free parameters.

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Energy conditions in \(f(\mathcal {G},T)\) gravity

Eur. Phys. J. C Energy conditions in f (G , T ) gravity M. Sharif 0 Ayesha Ikram 0 0 Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus , Lahore 54590 , Pakistan The aim of this paper is to introduce a new modified gravity theory named f (G, T ) gravity (G and T are the Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively) and investigate energy conditions for two reconstructed models in the context of FRW universe. We formulate general field equations, divergence of energymomentum tensor, equation of motion for test particles as well as corresponding energy conditions. The massive test particles follow non-geodesic lines of geometry due to the presence of an extra force. We express the energy conditions in terms of cosmological parameters like the deceleration, jerk, and snap parameters. The reconstruction technique is applied to this theory using de Sitter and power-law cosmological solutions. We analyze the energy bounds and obtain feasible constraints on the free parameters. - Current cosmic accelerated expansion has been affirmed from a diverse set of observational data coming from several pieces of astronomical evidence, including supernova type Ia, large scale structure, cosmic microwave background radiation etc. [1–4]. This expanding paradigm is considered as a consequence of mysterious force dubbed dark energy (DE), which possesses a large negative pressure. Modified theories of gravity are considered as the favorite candidates to unveil the enigmatic nature of this energy. These modified theories are usually developed by including scalar invariants and their corresponding generic functions in the Einstein– Hilbert action. A remarkably interesting gravity theory is the modified Gauss–Bonnet (GB) theory. A linear combination of the form G = Rαβξη Rαβξη − 4Rαβ Rαβ + R2, a e-mail: b e-mail: where Rαβξη, Rαβ and R represent the Riemann tensor, the Ricci tensor, and the Ricci scalar, respectively, is called a Gauss–Bonnet invariant (G). It is a second order Lovelock scalar invariant and thus free from spin-2 ghosts instabilities [5–7]. The Gauss–Bonnet combination is a four-dimensional topological invariant which does not involve the field equations. However, it provides interesting results in the same dimensions when either coupled with a scalar field or when an arbitrary function f (G) is added to the Einstein–Hilbert action [8–10]. The latter approach is introduced by Nojiri and Odintsov; it is known as the f (G) theory of gravity [11]. Like other modified theories, this theory is an alternative to study DE and is consistent with solar system constraints [12]. In this context, there is a possibility to discuss a transition from decelerated to accelerated as well as from non-phantom to phantom phases and also to explain the unification of early and late times accelerated expansion of the universe [13,14]. The fascinating problem of cosmic accelerated expansion has successfully been discussed by taking into account modified theories of gravity with curvature–matter coupling. The motion of test particles is studied in f (R) and f (G) gravity theories non-minimally coupled with the matter Lagrangian density (Lm ). Consequently, the extra force experienced by test particles is found to be orthogonal to their four velocities and the motion becomes non-geodesic [15–17]. It is found that, for certain choices of Lm , the presence of the extra force vanishes in a non-minimal f (R) model, while it remains preserved in a non-minimal f (G) model. The geodesic deviation is weaker in f (G) gravity for small curvatures as compared to non-minimal f (R) gravity. Nojiri et al. [18] studied the nonminimally coupling of f (R) and f (G) theories with Lm and found that such a coupling naturally unifies the inflationary era with current cosmic accelerated expansion. In order to describe some realistic matter distribution, certain conditions must be imposed on the energy-momentum tensor (Tαβ ) known as energy conditions. These conditions originate from the Raychaudhuri equations with the requirement that not only gravity is attractive but also the energy density is positive. The null (NEC), weak (WEC), dominant (DEC), and strong (SEC) energy conditions are the four fundamental conditions. They play a key role to study the theorems related to singularity and black hole thermodynamics. The null energy condition is important to discuss the second law of black hole thermodynamics while its violation leads to a Big-Rip singularity of the universe [19]. The proof of the positive mass theorem is based on DEC [20], while SEC is useful to study the Hawking–Penrose singularity theorem [21]. The energy conditions have been investigated in different modified theories of gravity like f (R) gravity, Brans– Dicke theory, f (G) gravity, and generalized teleparallel theory [22–25]. Banijamali et al. [26] investigated the energy conditions for non-minimally coupling f (G) theory with Lm (...truncated)


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M. Sharif, Ayesha Ikram. Energy conditions in \(f(\mathcal {G},T)\) gravity, The European Physical Journal C, 2016, pp. 640, Volume 76, Issue 11, DOI: 10.1140/epjc/s10052-016-4502-1