Abstract
First, we prove that a Lorentzian manifold is of constant curvature if and only if W2-curvature tensor vanishes. We investigate W2-flat perfect fluid spacetime as a solution of fG-gravity theory and we obtain a relation among deceleration, jerk, and snap parameters in a W2-flat spacetime using Friedmann–Robertson–Walker metric. Several energy conditions in terms of Ricci scalar are investigated with the models fG=a1Gn+b1a2Gn+b2 and fG=log(αGn+βe−Gα). For these models, the weak, null and dominant energy conditions are satisfied, while the strong energy condition is violated, which is good agreement with the recent observational studies and this reveals that the current Universe is in accelerating phase.
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