Some time ago, we showed that a weak (linear) massless spin two wave could only propagate on a Ricci-flat or Ricci-constant background: it must necessarily be a perturbation of general relativity. This was just the continuation of the higher spin chain: massless s = 3/2 also required Ricci-flatness (which is the basis of supergravity) while s > 2 needs Riemann flatness. This note, entitled ‘higher spin m ≠ 0 excitations on curved backgrounds and cosmological supergravity’, re-analyzes the problem in a perhaps more physical way: by considering massless and—only apparently—massive small excitations and showing how their parameters relate to the cosmological constant. We will thus prove, in a simple physical way, the necessity, as well as the sufficiency, of the known supergravity results.

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附录：关于在弯曲背景下自旋两个场的注释（2007 年级。Quantum Grav. 24 1683）

前段时间，我们证明了弱（线性）无质量自旋二次波只能在 Ricci 平面或 Ricci 常数背景下传播：它必然是广义相对论的摄动。这只是更高自旋链的延续：无质量秒= 3/2 还需要 Ricci 平坦度（这是超引力的基础），而秒> 2 需要黎曼平坦度。这篇题为“更高的自旋”的笔记米≠ 0 excitations on curved backgrounds and cosmological supergravity'，以一种可能更物理的方式重新分析了这个问题：通过考虑无质量和——只是表面上——有质量的小激发，并展示它们的参数如何与宇宙学常数相关。因此，我们将以简单的物理方式证明已知超引力结果的必要性和充分性。