Tree-level Scattering Amplitude in de Sitter Space

In previous papers [1,2], it was proved that a covariant quantization of the minimally coupled scalar field in de Sitter space is achieved through addition of the negative norm states. This causal approach which eliminates the infrared divergence, was generalized further to the calculation of the graviton propagator in de Sitter space [3] and one-loop effective action for scalar field in a general curved space-time [4]. This method gives a natural renormalization of the above problems. Pursuing this approach, in the present paper the tree-level scattering amplitudes of the scalar field, with one graviton exchange, has been calculated in de Sitter space. It is shown that the infrared divergence disappears and the theory automatically reaches a renormalized solution of the problem.