Conformal graviton two-point function in de Sitter space

The conformally invariant linearized de Sitter gravitational wave equation has recently received a lot of attention. In this article, using the ambient space notations, we solve this field equation in five various cases. In each case, it has been shown that the solution can be written as the product of a generalized symmetric polarization tensor of rank 2 and a massless minimally or conformally coupled scalar field in de Sitter space-time. The conformally covariant graviton two-point functions have been calculated in terms of the massless minimally or conformally coupled scalar two-point functions, using ambient space notations. In the case of massless minimally coupled scalar field, the Krien space quantization has been used to avoid the violation of de Sitter invariance. The two-point functions are expressed in terms of de Sitter intrinsic coordinates from their ambient space counterparts, which are free of any theoretical problem.