Abstract
In previous papers (De Bièvre S. and Renaud J.,Phys. Rev. D 57 (1998) 6230; Gazeau J. P., Renaud J.and Takook M. V., Class. Quantum Grav. 17 (2000) 1415,gr-qc/9904023), it was proved that a covariant quantization ofthe minimally coupled scalar field in de Sitter space is achievedthrough addition of the negative norm states. This causal approach,which eliminates the infrared divergence, was generalized furtherto the calculation of the graviton propagator in de Sitter space(Takook M. V., Proceedings of the Wigsym6, 16-22 August1999, Istanbul, Turkey (gr-qc/0001052)) and one-loop effectiveaction for scalar field in a general curved space-time (Takook M. V., Natural renormalized one-loop effective actionfor the scalar field in a curved space-time, gr-qc/0006052, to bepublished in Int. J. Mod. Phys. E (2004)). This methodgives a natural renormalization of the above problems. Pursuingthis approach, in the present paper the tree-level scatteringamplitudes of the scalar field, with one graviton exchange, havebeen calculated in de Sitter space. It is shown that the infrareddivergence disappears and the theory automatically reaches arenormalized solution of the problem.
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