Conformally invariant wave-equations and massless fields in de Sitter spacetime

TL;DR

This paper introduces conformally invariant wave equations for scalar and vector fields in de Sitter space, computes their solutions and two-point functions, and explores their properties and limits in a coordinate-independent framework.

Contribution

It presents new conformally invariant wave equations in de Sitter space and provides explicit solutions, two-point functions, and a detailed analysis of their properties and limits.

Findings

Solutions and two-point functions for conformally invariant fields were calculated.

The Hilbert space structure and field operators were explicitly constructed.

Minkowskian limits of the solutions were analyzed.

Abstract

Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been calculated. The ``Hilbert'' space structure and the field operator, in terms of coordinate independent de Sitter plane waves, have been defined. The construction of the paper is based on the analyticity in the complexified pseudo-Riemanian manifold, presented first by Bros et al.. Minkowskian limits of these functions are analyzed. The relation between the ambient space notation and the intrinsic coordinates is then studied in the final stage.