Perturbative <i>S</i>-matrix unitarity (S†S = 1) in Rμν2 gravity

We show that in the quadratic curvature theory of gravity, or simply $R_{\mu \nu} ^2$ tree-level unitariy bound (tree unitarity) is violated UV region but an analog for $S$-matrix unitarity ($SS^{\dagger} = 1$) satisfied. This renormalizable, and hence failure tree a counter example Llewellyn Smith's conjecture on relation between them. have recently proposed new gives same conditions as renormalizability. verify holds matter-graviton scattering at level demonstrating our conjecture.