We study scalar field theories invariant under transverse diffeomorphisms in cosmological contexts. We show that in the geometric optics approximation, the corresponding particles move along geodesics and contribute with the same active mass (energy) to the gravitational field as in Diff invariant theories. However, for low-frequency (super-Hubble) modes, the contributions to the energy-momentum tensor differ from that of Diff invariant theories. This opens up a wide range of possibilities for cosmological model building. As an example, we show that the simplest TDiff invariant scalar field theory with only kinetic term could drive inflation and generate a nearly scale invariant (red-tilted) spectrum of density fluctuations. We also present a detailed analysis of cosmological perturbations and show that the breaking of full Diff invariance generically induces new non-adiabatic pressure perturbations. A simple scalar field dark matter model based on a purely kinetic term that exhibits the same clustering properties as standard cold dark matter is also presented.

中文翻译：

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宇宙学的 TDiff 不变场论

我们研究宇宙学背景下横向微分同胚下不变的标量场论。我们证明，在几何光学近似中，相应的粒子沿着测地线移动，并对引力场贡献与 Diff 不变理论中相同的活性质量（能量）。然而，对于低频（超哈勃）模式，对能量动量张量的贡献与 Diff 不变理论不同。这为宇宙学模型的构建开辟了广泛的可能性。作为一个例子，我们证明了最简单的 TDiff 不变标量场理论（仅包含动力学项）可以驱动膨胀并生成几乎尺度不变（红色倾斜）的密度涨落谱。我们还对宇宙学扰动进行了详细分析，并表明，完全 Diff 不变性的破坏通常会引起新的非绝热压力扰动。还提出了一种基于纯动力学项的简单标量场暗物质模型，该模型表现出与标准冷暗物质相同的聚类特性。