Europhys. Lett., 68 (1), pp. 15-18 (2004)
DOI: 10.1209/epl/i2004-10217-3

Tree-level scattering amplitude in de Sitter space

S. Rouhani¹ and M. V. Takook<sup>1, 2

1</sup>  Plasma Physics Research Centre, Islamic Azad University P.O. Box 14835-157, Teheran, Iran
²  Department of Physics, Razi University - Kermanshah, Iran

takook@razi.ac.ir

received 26 January 2004; accepted in final form 6 August 2004

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 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 (TAKOOK M. V., Proceedings of the Wigsym6, 16-22 August 1999, Istanbul, Turkey (gr-qc/0001052)) and one-loop effective action for scalar field in a general curved space-time (TAKOOK M. V., Natural renormalized one-loop effective action for the scalar field in a curved space-time , gr-qc/0006052, to be published in Int. J. Mod. Phys. E (2004)). 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, have 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.

PACS
04.62.+v - Quantum field theory in curved spacetime.
98.80.Cq - Particle-theory and field-theory models of the early Universe (including cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe, etc.).
12.10.Dm - Unified theories and models of strong and electroweak interactions.

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