Impact of quasi-conformal curvature tensor in spacetimes and f (R, G)-gravity

At first, we showthat a quasi-conformally flat perfect fluid spacetime is a de-Sitter spacetime aswell as a Robertson-Walker spacetime. We study this spacetime as a solution of f (R, G)-gravity theory, and obtain a relation among snap, jerk, and deceleration parameters using flat Friedmann-Robertson-Walker metric. Several energy conditions in terms of Ricci scalar are investigated with the models f (R, G) = mu R(beta 1)G(beta 2), f (R, G) + alpha R-1 + alpha(2)RmGn and f (R, G) = R + a(1)G(alpha 3). For these models, the weak, null and dominant energy conditions are satisfied while the strong energy condition is violated, which is a good agreement with the recent observational studies which reveals that the current Universe is in accelerating phase.