Conformally related massless fields in dS, AdS and Minkowski spaces

TL;DR

This paper derives a unified equation for conformally coupled scalar fields across dS, AdS, and Minkowski spaces, simplifying the analysis of curvature effects and limits, and introduces de Sitter plane waves that reduce to standard plane waves in flat space.

Contribution

It provides a unified formulation of conformally coupled scalar fields in various spacetimes and introduces de Sitter plane waves that connect to flat space solutions.

Findings

Unified scalar field equation for dS, AdS, and Minkowski spaces.

Simple curvature dependence via a conformal factor.

De Sitter plane waves reduce to standard plane waves in flat space.

Abstract

In this paper we write down the equation for a scalar conformally coupled field simultaneously for de Sitter (dS), anti-de Sitter (AdS) and Minkowski spacetime in d-dimensions. The curvature dependence appears in a very simple way through a conformal factor. As a consequence the process of curvature free limit, including wave functions limit and two-points functions, turns to be a straightforward issue. We determine a set of modes, that we call de Sitter plane waves, which become ordinary plane waves when the curvature vanishes.