A Group Theoretical Approach to Graviton Two-Point Function

TL;DR

This paper develops a group theoretical framework for linear conformal gravity in de Sitter space, deriving a tensor field solution and a two-point function that is invariant and free of infrared divergence.

Contribution

It introduces a tensor field of rank-3 with mixed symmetry for conformal gravity and computes a de Sitter invariant two-point function free of infrared divergence.

Findings

Derived a proper solution to the physical part of the field equation.

Calculated a de Sitter invariant two-point function.

The two-point function is free of infrared divergence.

Abstract

Respecting the group theoretical approach, it is debated that the theory of linear conformal gravity should be formulated through a tensor field of rank-3 and mixed symmetry \cite{binegar}. Pursuing this path, such a field equation was obtained in de Sitter space \cite{takook}. In present work, considering the de Sitter ambient space notation, a proper solution to the physical part of this field equation is obtained. We have also calculated the related two-point function, which is interestingly de Sitter invariant and free of infrared divergence.