Abstract
The linearized gravitational field equation in de Sitter (dS) four-dimensional space is gauge invariant under some special gauge transformations. It is also gauge invariant in ambient space notations in which the field equation is written in terms of the Casimir operators of dS group. In this paper the field equation is solved in terms of a gauge-fixed value (i.e. in the minimal case). It is shown that the solution can be written as the multiplication of a generalized symmetric rank-2 polarization tensor and a massless minimally coupled scalar field in ambient space notations. The two-point function is calculated in ambient space notations, which is dS-invariant and free of any divergences. This two-point function has been expressed in terms of dS intrinsic coordinates, from its ambient space counterpart, which is clearly dS-invariant and free of any divergences again.
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