 Linearized f(R) gravity about Minkowski spacetime

If $f(0)=0$, $f^{\prime }(0)=1$, and $f^{\prime \prime }(0)=0$, then $f(R)=R+O(R^3)$ near zero. The field equations linearized about Minkowski spacetime are therefore the Linearized Einstein equations; deviations first appear beyond linear order.