Conformal Auxiliary "Massless" Spin-2 Field in de Sitter Space

TL;DR

This paper investigates a conformal auxiliary spin-2 field in de Sitter space, analyzing its solutions and conformally invariant two-point function, contributing to the understanding of conformal gravity in curved spacetime.

Contribution

It provides a detailed study of the auxiliary tensor field's solutions and conformally invariant two-point function in de Sitter space, expanding the understanding of conformal gravity.

Findings

Identified solutions for the auxiliary spin-2 field in de Sitter space.

Derived the conformally invariant two-point function for the field.

Connected the auxiliary field's properties to unitary irreducible representations of the de Sitter group.

Abstract

Respecting the group theoretical approach, it is discussed that the linear conformal gravity can be written in terms of a mixed symmetry tensor field of rank-3 \cite{binegar}. Following this path, related field equation was obtained in de Sitter space \cite{fatemi}. It was proved that this kind of tensor field in de Sitter background associates with two unitary irreducible representations (UIR) of the de Sitter group. The important fact is that one of the them has a flat limit, namely, in zero curvature coincides to the UIR of Poincar\'{e} group which has been studied in Ref \cite{rahbar}. However, the second one which is named as auxiliary field, becomes significant in the study of conformal gravity in de Sitter background. In this paper we will study the second representation in details by finding its solutions and also the conformally invariant two-point function.