Characterizations of quasi-Einstein spacetimes and f(ℛ,G)-gravity.

First, we illustrate that a Ricci symmetric quasi-Einstein spacetime is a static spacetime and belongs to Petrov classification I , D or O. We investigate conformally flat quasi-Einstein spacetime as a solution of f (ℛ , G) -gravity theory and explain the physical meaning of the Friedmann–Robertson–Walker metric. For the models f (ℛ , G) = μ ℛ β 1 G β 2 , ( β 1 , β 2 and μ are constants) and f (ℛ , G) = ℛ 2 − 6 G , various energy conditions in terms of associated scalars are examined. These models satisfy the weak, null, and dominant energy conditions, while violating the strong energy condition, which is in good agreement with recent empirical investigations that show the Universe is currently in an accelerating phase. [ABSTRACT FROM AUTHOR]