Conformal linear gravity in de Sitter space

TL;DR

This paper derives a sixth-order field equation for a symmetric tensor field in de Sitter space, linking conformal linear gravity with tensor fields of different ranks through homomorphisms, advancing the understanding of quantum gravity models.

Contribution

It introduces a sixth-order field equation for the graviton-related tensor field in de Sitter space, connecting conformal gravity with tensor representations via homomorphisms.

Findings

Derived the field equation of order 6 for the tensor field in de Sitter space.

Established homomorphisms between rank-3 mixed symmetry and rank-2 symmetric tensor fields.

Linked conformal invariance with unitary irreducible representations in de Sitter space.

Abstract

It has been shown that the theory of linear conformal quantum gravity must include a tensor field of rank-3 and mixed symmetry [1]. In this paper, we obtain the corresponding field equation in de Sitter space. Then, in order to relate this field with the symmetric tensor field of rank-2, $\K_{\alpha\beta}$ related to graviton, we will define homomorphisms between them. Our main result is that if one insists $\K_{\alpha\beta}$ to be a unitary irreducible representation of de Sitter and conformal groups it must satisfy a filed equation of order 6, which is obtained.