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First and foremost, we show that a 4‐dimensional conformally flat generalized Ricci recurrent spacetime(  G  R  )   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  +   Gand    f   (  R  ,  G  )   =   R  2   +  G  l  n  G   . 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.

How a Conformally Flat ( G R ) 4 Impacts Gauss‐Bonnet Gravity?