We study a theory of minimally modified gravity called cuscuton/VCDM that propagates only two gravitational degrees of freedom. Despite being apparently different from general relativity (GR), it is in principle possible that this theory might be obtained via a field redefinition starting from the GR action. This would make the vacuum theory equivalent to GR and the theory would differ from GR only in the presence of matter. In this paper, studying the dispersion relation of gravitational waves and the dynamics of the Bianchi-I universe, we prove that such a field redefinition does not exist and that the theory differs from GR already in vacuum.

中文翻译：

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无质量横向无迹引力子的非唯一性

我们研究了一种称为 cuscuton/VCDM 的最小修正重力理论，它仅传播两个重力自由度。尽管与广义相对论 (GR) 明显不同，但原则上可能通过从 GR 作用开始的场重新定义来获得该理论。这将使真空理论等同于 GR，并且该理论仅在物质存在时与 GR 不同。在本文中，通过研究引力波的色散关系和比安奇一宇宙的动力学，我们证明了这样的场重新定义不存在，并且该理论与已经在真空中的GR不同。