Massive scalar field on (A)dS space from a massless conformal field in $\mathbb{R}^6$

TL;DR

This paper demonstrates how scalar field equations on (A)dS spaces can be derived from a conformal field in six-dimensional space, emphasizing geometric constraints and invariance properties.

Contribution

It provides a unified geometric framework to obtain scalar field equations on (A)dS spaces from a massless conformal field in -dimensional space, highlighting the role of symmetry and constraints.

Findings

Scalar field equations on (A)dS spaces derived from D conformal field.

Geometric constraints in D space suffice to obtain (A)dS equations.

SO(2,4) invariance underpins the derivation process.

Abstract

We show how the equations for the scalar field (including the massive, massless, minimally and conformally coupled cases) on de Sitter and Anti-de Sitter spaces can be obtained from both the SO$(2,4)$-invariant equation $\square \phi = 0$ in $\mathbb{R}^6$ and two geometrical constraints defining the (A)dS space. Apart from the equation in $\mathbb{R}^6$, the results only follow from the geometry.