Linear Weyl Gravity in de Sitter Universe

TL;DR

This paper derives the linear form of Weyl gravity in a de Sitter universe, explores its representation in five-dimensional space, and analyzes its group theoretical properties, revealing it does not form a unitary irreducible representation.

Contribution

The paper presents the first derivation of linear Weyl gravity in de Sitter space and examines its group theoretical properties in five-dimensional ambient space.

Findings

Linear Weyl gravity in de Sitter space is obtained.

The linear form does not correspond to a unitary irreducible representation of the de Sitter group.

The ambient space notation for this theory is established.

Abstract

In this paper we obtain the linear Weyl gravity in de Sitter background. Its linear form in five-dimensional ambient space notation has also been obtained. From the group theoretical point of view, we show that this conformal invariant fourth order theory in its linear form does not transform as an unitary irreducible representation of the de Sitter group.