Abstract
The aim of this paper is to introduce a new modified gravity theory named as $f(\mathcal{G},T)$ 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 extra force. We express energy conditions in terms of cosmological parameters like deceleration, jerk and snap parameters. The reconstruction technique is applied to this theory using de Sitter and power-law cosmological solutions. We analyze energy bounds and obtain feasible constraints on free parameters.
Highlights
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. [1,2,3,4]
This expanding paradigm is considered as a consequence of mysterious force dubbed dark energy (DE), which possesses a large negative pressure
We introduced a new modified theory of gravity named f (G, T ) gravity, in which the gravitational Lagrangian is obtained by adding a generic function f (G, T ) in the Einstein–Hilbert action
Summary
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. [1,2,3,4]. 2, we formulate the field equations of this gravity and discuss the equation of motion for test particles, while general expressions for the energy conditions as well as formulations in terms of cosmological parameters are discussed in Sect. We formulate the field equations for f (G, T ) gravity For this purpose, we assume an action of the following form: S. where g and κ represent the determinant of the metric tensor (gαβ ) and the coupling constant, respectively. T yield δG = 2Rδ R − 4δ(Rαβ Rαβ ) + δ(Rαβξη Rαβξη), δT = (Tαβ + αβ )δgαβ , αβ gξ η δ Tξ η δgαβ (6) Using these variational relations in Eq (4), we obtain the field equations of f (G, T ) gravity after simplification as follows: Gαβ = κ2Tαβ − The equation of motion for a perfect fluid in general relativity is recovered in the absence of coupling between matter and geometry [32]
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