Symmetries, conservation laws, reductions, and exact solutions for the Klein-Gordon equation in de Sitter space-times

In this paper, we complement the analysis involving the 'fundamental' solutions of the Klein-Gordon equation in de Sitter space-times given by Yagdjian and A. Galstian (Comm. Math. Phys. 285, 293 (2009); Discrete and Continuous Dynamical Systems S, 2(3), 483 (2009)). Using the symmetry generators, we classify and reduce the underlying equations and show how this process may lead to exact solutions by quadratures. PACS Nos: 04.25.-g, 02.30.Hq, 02.30.Jr, 02.40.-k Nous completons ici l'analyse impliquant les solutions fondamentales de l'equation de Klein-Gordon dans un espace-temps de de Sitter, rapportees par Yagdjian et Galstian (Comm. Math. Phys. 285, 293 (2009); Discrete and Continuous Dynamical Systems S, 2(3), 483 (2009)). Utilisant les generateurs de symetrie, nous classifions et reduisons les equations sous-jacentes et montrons comment ce processus peut mener aux solutions exactes par quadratures. [Traduit par la Redaction]
1. Introduction The Einstein theory of general relativity is a field theory of gravitation [1]. The equations that represent the theory are known as Einstein field equations [R.sub.[mu]v] - 1/2 [...]