Conformal linear gravity in de Sitter space II

TL;DR

This paper develops a conformally invariant linear gravity theory in de Sitter space using a rank-3 tensor field, providing explicit solutions and a well-behaved two-point function that respects de Sitter symmetry.

Contribution

It derives a proper solution for the conformal gravity field equation in de Sitter space and computes a de Sitter invariant two-point function free of large-distance pathology.

Findings

Solution expressed as a product of polarization tensor and scalar field

Two-point function is de Sitter invariant

Two-point function is free of large-distance divergences

Abstract

From the group theoretical point of view, it is proved that the theory of linear conformal gravity should be written in terms of a tensor field of rank-3 and mixed symmetry [Binegar, et al, Phys. Rev. D 27, (1983) 2249]. We obtained such a field equation in de Sitter space [Takook, et al, J. Math. Phys. 51, (2010) 032503]. In this paper, a proper solution to this equation is obtained as a product of a generalized polarization tensor and a massless scalar field and then the conformally invariant two-point function is calculated. This two-point function is de Sitter invariant and free of any pathological large-distance behavior.