Impact of quasi-constant curvature in f (R, G) and f (R, T)-gravity

In this article it is illustrated that a spacetime of quasi-constant curvature is a static spacetime as well as generalized Robertson-Walker spacetime under certain restrictions on the associated scalars. As a consequence, we prove that such a spacetime becomes a Robertson-Walker spacetime and belongs to Petrov classification I, D or O. We investigate this spacetime as a solution of f (R, G)-gravity and f (R, T)-gravity theories and describe the physical explanation of the Friedmann-Robertson-Walker metric. With the models f (R, G) = 2R + λG (λ is constant) and f (R, T) = R + 2T, several energy conditions in terms of associated scalars are explored.