Positive-energy theorem forR+R2gravity

We prove that asymptotically flat extrema of the action $S=\int [R+(\frac{1}{2{\beta }^2}\left)R^2\right]$ have non-negative energy, provided there exists a spacelike hypersurface on which $R>-{\beta }^2$. Flat space is shown to be the unique topologically Minkowskian stationary point of the energy. This result leads to a heuristic functional variational argument for positivity that does not involve restrictions on $R$. We also prove that flat space is semiclassically stable. Possible extensions of the theorems and relevance to quantum gravity are briefly discussed.