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In this paper we work in perturbative Quantum Gravity coupled to ScalarMatter at tree level and we introduce a new effective model in analogy with theFermi theory of weak interaction and in relation with a previous work where wehave studied only the gravity and its self-interaction. This is an extension ofthe I.T.B model (Intermediate-Tensor-Boson) for gravity also to gravitationalinteracting scalar matter. We show that in a particular gauge the infiniteseries of interactions containing "n" gravitons and two scalars could berewritten in terms of only two Lagrangians containing a massive field, thegraviton and, obviously, the scalar field. Using the S-matrix we obtain thatthe low energy limit of the amplitude reproduce the local Lagrangian for thescalar matter coupled to gravity.Comment: 7 pages Late

Tree level gravity?scalar matter interactions in analogy with Fermi theory of weak interactions using only a massive vector field