Auxiliary "massless" spin-2 field in de Sitter universe

TL;DR

This paper investigates an auxiliary 'massless' spin-2 field in de Sitter space, deriving its two-point function and exploring its conformal invariance and relation to different unitary irreducible representations.

Contribution

It introduces and analyzes an auxiliary 'massless' spin-2 field in de Sitter space using Dirac's six-cone formalism, highlighting its conformal invariance and de Sitter invariant two-point function.

Findings

Derived a de Sitter invariant two-point function for the auxiliary field

Connected the auxiliary field to the conformally coupled scalar field

Clarified the role of the auxiliary field in the representation theory of de Sitter space

Abstract

For the tensor field of rank-2 there are two unitary irreducible representation (UIR) in de Sitter (dS) space denoted by $\Pi^{\pm}_{2,2}$ and $\Pi^{\pm}_{2,1}$ [1]. In the flat limit only the $\Pi^{\pm}_{2,2}$ coincides to the UIR of Poincar\'e group, the second one becomes important in the study of conformal gravity. In the pervious work, Dirac's six-cone formalism has been utilized to obtain conformally invariant (CI) field equation for the "massless" spin-2 field in dS space [2]. This equation results in a field which transformed according to $\Pi^{\pm}_{2,1}$, we name this field the auxiliary field. In this paper this auxiliary field is considered and also related two-point function is calculated as a product of a polarization tensor and "massless" conformally coupled scalar field. This two-point function is de Sitter invariant.