Massive Spin-2 Field in De Sitter Space

TL;DR

This paper develops a covariant quantization method for a massive spin-2 field in de Sitter space, extending previous work on lower spins, and sets the stage for future analysis of massless spin-2 fields in quantum gravity.

Contribution

It introduces a coordinate-independent covariant quantization framework for the massive spin-2 field on de Sitter space, based on Wightman-Garding axioms and analyticity conditions.

Findings

Quantization procedure established for massive spin-2 in dS

Framework compatible with massless spin-2 limit

Preparation for quantum gravity applications

Abstract

In this paper we present a covariant quantization of the ``massive'' spin-2 field on de Sitter (dS) space. By ``massive'' we mean a field which carries a specific principal series representation of the dS group. The work is in the direct continuation of previous ones concerning the scalar, the spinor and the vector cases. The quantization procedure, independent of the choice of the coordinate system, is based on the Wightman-Garding axiomatic and on analyticity requirements for the two-point function in the complexified pseudo-Riemanian manifold. Such a construction is necessary in view of preparing and comparing with the dS conformal spin-2 massless case (dS linear quantum gravity) which will be considered in a forthcoming paper and for which specific quantization methods are needed.