  First and foremost, we show that a 4-dimensional conformally flat generalized
Ricci recurrent spacetime $(GR)_4$ is an Einstein manifold. We examine such a
spacetime as a solution of $f(R, G)$-gravity theory and it is shown that the
additional terms from the modification of the gravitational sector can be
expressed as a perfect fluid. Several energy conditions are investigated with
$f(R, G) = R +\sqrt{G}$ and $f(R, G) = R^2+GlnG$. For both the models, weak,
null and dominant energy conditions are satisfied while 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.
