  In this paper, the two-point function of linearized gravitons on de Sitter
(dS) space is presented. Technically, respecting the dS ambient space notation,
the field equation is given by the coordinate-independent Casimir operators of
the de Sitter group. Analogous to the quantization of the electromagnetic field
in Minkowski space, the field equation admits gauge solutions. The notation
allows us to exhibit the formalism of Gupta-Bleuler triplets for the present
field in exactly the same manner as it occurs for the electromagnetic field. In
this regard, centering on the spin-two part (the traceless part,
${\cal{K}}^t$), the field solution is written as a product of a generalized
polarization tensor and a minimally coupled massless scalar field. Then,
admitting a de Sitter-invariant vacuum through the so-called "Krein space
quantization", the de Sitter fully covariant two-point function is calculated.
This function is interestingly free of pathological large distance behavior
(infrared divergence). Moreover, the spin-zero part (the pure-trace part;
${\cal{K}}^{pt}$) of the field is discussed in this paper. It is shown that the
implications of the dS group unitary irreducible representations restrict the
gauge-fixing parameter to the optimal value, which remarkably results in the
pure-trace part be written in terms of a conformally coupled massless scalar
field.
