IMPACT OF QUASI-CONSTANT CURVATURE IN f (R, G) AND f (R, T )-GRAVITY

Abstract

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.