The inflationary universe creates particle pairs, which are entangled in their momenta due to momentum conservation. Operators involving the momenta of the fluctuations can be rewritten into pseudo-spin operators, such as the Gour-Khanna-Mann-Revzen (GKMR) pseudo-spin. Making use of these pseudo-spin operators, cosmological Bell inequalities can be formulated. The violation of these Bell inequalities indicates the quantum nature of primordial fluctuations. In this work, we focus on primordial curvature perturbations. Since curvature perturbations arise from gravity, their action includes the Gibbons-Hawking-York boundary term. We clarify the role of the boundary term in selecting suitable initial conditions for linear perturbations. After that, we proceed to the interactions of cosmological perturbations, including the bulk and boundary interaction terms, which introduce decoherence effects. These decoherence effects change the expectation value of the Bell operator, and gradually restore the Bell inequality. We describe this process by a “Bell test curve”, which offers a window around 5 e-folds for testing the quantum origin of cosmological perturbations. We also explore the possibility of extracting the information of the decoherence rate and the structure of primordial interactions from the Bell test curve.

中文翻译：

---

具有退相干效应的 Cosmological Bell 检验


膨胀宇宙会产生粒子对，由于动量守恒，这些粒子对被它们的动量纠缠在一起。涉及波动动量的算子可以改写为伪自旋算子，例如 Gour-Khanna-Mann-Revzen （GKMR） 伪自旋。利用这些伪自旋算子，可以公式化宇宙学贝尔不等式。违反这些贝尔不等式表明了原始涨落的量子性质。在这项工作中，我们专注于原始曲率扰动。由于曲率扰动是由引力引起的，因此它们的作用包括 Gibbons-Hawking-York 边界项。我们阐明了边界项在为线性扰动选择合适的初始条件中的作用。之后，我们继续研究宇宙学扰动的相互作用，包括引入退相干效应的本体和边界相互作用项。这些退相干效应改变了 Bell 算子的期望值，并逐渐恢复了 Bell 不等式。我们用“贝尔测试曲线”来描述这个过程，它提供了一个大约 5 个 e 折叠的窗口，用于测试宇宙学扰动的量子起源。我们还探索了从 Bell 检验曲线中提取退相干率和原始相互作用结构信息的可能性。