Conformally Invariant "Massless" Spin-2 Field in de Sitter Universe

TL;DR

This paper derives a conformally invariant massless spin-2 field equation in de Sitter space using group theory and Dirac's six-cone formalism, providing a de Sitter invariant graviton two-point function free of large-distance issues.

Contribution

It introduces a new conformally invariant equation for massless spin-2 fields in de Sitter space using a group theoretical approach and Dirac's six-cone formalism.

Findings

Derived the conformally invariant massless spin-2 field equation.

Obtained a de Sitter invariant graviton two-point function.

Quantized the physical sector using Krein space quantization.

Abstract

''Massless'' spin-2 field equation in de Sitter space, which is invariant under the conformal transformation, has been obtained. The frame work utilized is the symmetric rank-2 tensor field of the conformal group. Our method is based on the group theoretical approach and six-cone formalism, initially introduced by Dirac. Dirac's six-cone is used to obtain conformally invariant equations on de Sitter space. The solution of the physical sector of massless spin-2 field (linear gravity) in de Sitter ambient space is written as a product of a generalized polarization tensor and a massless minimally coupled scalar field. Similar to the minimally coupled scalar field, for quantization of this sector, the Krein space quantization is utilized. We have calculated the physical part of the linear graviton two-point function. This two-point function is de Sitter invariant and free of pathological large distance behavior.