Cosmological reconstruction and energy bounds in \(f(R,R_{\alpha \beta }R^{\alpha \beta },\phi )\) gravity

The European Physical Journal C, May 2016

We discuss the cosmological reconstruction of \(f(R,R_{\alpha \beta }R^{\alpha \beta },\phi )\) (where R, \(R_{\alpha \beta }R^{\alpha \beta }\), and \(\phi \) represent the Ricci scalar, the Ricci invariant, and the scalar field) corresponding to a power law and de Sitter evolution in the framework of the FRW universe model. We derive the energy conditions for this modified theory which seem to be more general and can be reduced to some well-known forms of these conditions in general relativity, Open image in new window and \(f(R,\phi )\) theories. We have presented the general constraints in terms of recent values of the snap, jerk, deceleration, and Hubble parameters. The energy bounds are analyzed for reconstructed as well as known models in this theory. Finally, the free parameters are analyzed comprehensively.

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Cosmological reconstruction and energy bounds in \(f(R,R_{\alpha \beta }R^{\alpha \beta },\phi )\) gravity

Eur. Phys. J. C Cosmological reconstruction and energy bounds in f ( R, Rαβ Rαβ , φ) gravity M. Zubair 0 Farzana Kousar 0 0 Department of Mathematics, COMSATS Institute of Information Technology Lahore , Lahore , Pakistan We discuss the cosmological reconstruction of f (R, Rαβ Rαβ , φ) (where R, Rαβ Rαβ , and φ represent the Ricci scalar, the Ricci invariant, and the scalar field) corresponding to a power law and de Sitter evolution in the framework of the FRW universe model. We derive the energy conditions for this modified theory which seem to be more general and can be reduced to some well-known forms of these conditions in general relativity, f (R) and f (R, φ) theories. We have presented the general constraints in terms of recent values of the snap, jerk, deceleration, and Hubble parameters. The energy bounds are analyzed for reconstructed as well as known models in this theory. Finally, the free parameters are analyzed comprehensively. 1 Introduction In current cosmic picture dark energy (DE) is introduced as an effective characteristic which tends to accelerate the expansion in universe. Modified theories have achieved significant attention to explore the effect of cosmic acceleration [1]. These models have been developed to distinguish the source of DE as a modification to the Einstein Hilbert action. Some modified theories of gravity are f (R) gravity with Ricci scalar R [2], f (T ) gravity with torsion scalar T [3], Gauss–Bonnet gravity with G invariant [4], f (R, T ) gravity with T as the trace of the stress-energy tensor [5–14], f (R, T , Rμν )T μν [15–17] and f (R, G) gravity that contains both R and G [18] etc. The acceleration of the expanding universe can be explored by these theories through their corresponding invariants. To generalize Einstein’s theory of general relativity (GR), there is a vast literature on relativistic theories that reduce to GR in the proper limitations. An especially attractive class of these generalizations are the fourth-order theories. These theories were initially considered by Eddington in the early 1920s [19]. Whatever the inspiration to examine the generalized fourth-order theories, it is necessary to understand their weak-field limit, and these limits confirm the increasing behavior of these theories in observational data. Generally a fourth-order theory of gravity is obtained by adding Rab Rab and Rabcd Rabcd in the standard Einstein Hilbert action [20,21]. However, it is now established that we can ignore the Rabcd Rabcd term if we use the Gauss– Bonnet theorem [22]. About half a century ago, Brans and Dicke (BD) [23] presented the scalar–tensor theory of gravitation, which is still popular and has received great interest in cosmological dynamics as a replacement to dark matter and dark energy theories. The motivation behind the BD theory was Mach’s idea [24] to present a varying gravitational constant in general relativity. Among the theories alternative to Einstein’s gravity, the simplest and best known is Brans– Dicke theory. In this theory, the gravitational constant has been taken to be inversely proportional to the scalar field φ. The BD theory may be represented as a generalization of f (R) theory with f (R) = F (R) = φ R [2]. In modified theories, cosmological reconstruction is one of the important prospects in cosmology. In f (R) gravity, the reconstruction scheme has been used in different contexts to explain the conversion of the matter dominated era to the DE phase. This can be examined by considering the known cosmic evolution and the field equations are used to calculate a particular form of the Lagrangian which can reproduce the given evolution background. In these theories the existence of exact power law solutions for the FRW spacetime has been examined. In [25–27] the authors have reconstructed f (R, T ) gravity models by employing various cosmological scenarios. Nojiri et al. developed f (R) gravity models [28], which were further applied to f (R, G) and modified Gauss– Bonnet theories [29]. To reconstruct f (R) gravity models, Carloni et al. [30] have established a new technique by using the cosmic parameters instead of using a scale factor. Energy conditions are necessary to study the singularity theorems; moreover, we have the theorems related to black hole thermodynamics. For example, the well-known Hawking–Penrose singularity theorems [31] invoke the null energy condition (NEC) as well as the strong energy condition (SEC). The violation of SEC allows one to observe the accelerating expansion, and NECs are involved in the proof of the second law of black hole thermodynamics. The energy conditions have been explored in different contexts like f (T ) theory [32,33], f (R) gravity [34], and f (G) theory [35], Brans–Dicke theory [36]. Further the energy conditions of a very generalized second-order scalar–tensor gravity have been discussed by Sharif and Saira [37]. Sharif and Zubair have examined these conditions for f (R, T ) (...truncated)


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M. Zubair, Farzana Kousar. Cosmological reconstruction and energy bounds in \(f(R,R_{\alpha \beta }R^{\alpha \beta },\phi )\) gravity, The European Physical Journal C, 2016, pp. 254, Volume 76, Issue 5, DOI: 10.1140/epjc/s10052-016-4104-y