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We show how the recently introduced "Pure Connection Formulation" of gravityprovides a natural framework for approaching the problem of computing gravitonscattering amplitudes. In particular, we show that the interaction vertices aregreatly simplified in this formalism as compared to the Einstein-Hilbertperturbation theory. This, in turns, leads to very simple Feynman rules that weemploy for the direct computations. Furthermore, this framework naturallyextends to wider class of gravitational theories, which encompasses GeneralRelativity as a special case. We compute all the possible tree-levelgraviton-graviton scattering amplitudes for a general theory from this class.In the GR case the results are in complete accordance with the knownexpressions in the literature. Moreover, for the general theory distinct fromGR, we find new tree-level parity-violating amplitudes. The presence of thisnew amplitudes is a direct consequence of the fact that the general theory doesnot exhibit explicit parity invariance.

Graviton scattering amplitudes and Pure Connection Formulation of GR