In the present paper, we explore the possible effects of a second rank antisymmetric tensor field, known as Kalb-Ramond (KR) field, on cosmological particle production as well as on quantum entanglement for a massive scalar field propagating in a four dimensional FRW spacetime evolves through a symmetric bounce. For this purpose, the scalar field is considered to be coupled with the KR field and also with the Ricci scalar via the term $\sim \xi R\Phi^2$ (with $\xi$ be the coupling). The presence of KR field spoils the conformal symmetry of a massless scalar field even for $\xi = 1/6$ in four dimensional context, which has interesting consequences on particle production and consequently on quantum entanglement as we will discuss. In particular, the presence of KR field in a FRW bouncing universe allows a greater particle production and consequently the upper bound of the entanglement entropy becomes larger in comparison to the case when the KR field is absent. This may provide an interesting testbed for the existence of Kalb-Ramond field in our universe.

中文翻译：

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宇宙量子纠缠 : Kalb-Ramond 场存在的可能试验台

在本文中，我们探讨了称为 Kalb-Ramond (KR) 场的二阶反对称张量场对宇宙粒子产生以及在四维 FRW 时空传播的大规模标量场的量子纠缠的可能影响通过对称反弹演变。为此，标量场被认为与 KR 场以及 Ricci 标量通过术语 $\sim \xi R\Phi^2$ 耦合（其中 $\xi$ 是耦合）。KR 场的存在破坏了无质量标量场的共形对称性，即使在四维环境中 $\xi = 1/6$，这对粒子产生以及随后的量子纠缠具有有趣的影响，正如我们将讨论的那样。特别是，与 KR 场不存在的情况相比，FRW 弹跳宇宙中 KR 场的存在允许产生更大的粒子，因此纠缠熵的上限变得更大。这可能为我们宇宙中 Kalb-Ramond 场的存在提供一个有趣的试验台。