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In this brief note we present a somewhat trivial result. Namely, we show thatperturbative off-shell $f(R)$-theory is equivalent to Einstein gravity, as wellas to the Brans-Dicke theory and the Einstein scalar field model. We alsodiscuss possible generalisation of this result to higher-order gravitationalfield models.

On the equivalence between $ f\left(R\right) $ theories and Einstein gravity