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The solution to the linearized Einstein equation in de Sitter (dS) spacetimeand the corresponding two-point function are explicitly written down in a gaugewith two parameters `$a$' and `$b$'. The quantization procedure, independent ofthe choice of the coordinate system, is based on a rigorous group theoreticalapproach. Our result takes the form of a universal spin-two(transverse-traceless) sector and a gauge-dependent spin-zero (pure-trace)sector. Scalar equations are derived for the structure functions of each part.We show that the spin-two sector can be written as the resulting action of asecond-order differential operator (the spin-two projector) on a masslessminimally coupled scalar field (the spin-two structure function). The operatorplays the role of a symmetric rank-$2$ polarization tensor and has a spacetimedependence. The calculated spin-two projector grows logarithmically withdistance and also no dS-invariant solution for either structure functionsexist. We show that the logarithmically growing part and the dS-breakingcontribution to the spin-zero part can be dropped out, respectively, forsuitable choices of parameters `$a$' and `$b$'. Considering thetransverse-traceless graviton two-point function, however, shows that dSbreaking is universal (cannot be gauged away). More exactly, if one wants torespect the covariance and positiveness conditions, the quantization of the dSgraviton field (as for any gauge field) cannot be carried out directly in aHilbert space and involves unphysical negative norm states. However, a suitableadaptation (Krein spaces) of the Gupta-Bleuler scheme for massless fields,based on the group theoretical approach, enables us to obtain the correspondingtwo-point function satisfying the conditions of locality, covariance,transversality, index symmetrizer, and tracelessness.

Covariant and infrared-free graviton two-point function in de Sitter spacetime II