论文标题
用量子场探测宇宙学奇点：开放和封闭的FLRW宇宙
Probing cosmological singularities with quantum fields: Open and closed FLRW universes
论文作者
论文摘要
最近指出的是，线性量子字段$ \ hat ϕ（x）$可以有意义地在空间平坦的弗里德曼，莱玛特，罗伯逊，沃克（flrw）Universes \ cite \ cite {adls2021}的大爆炸（和大键）上传播。回想一下，$ \ hat ϕ（x）$，以及重新归一化的观察值$ \ langle \ hat ϕ（x）^2 \ rangle_ {ren} $和$ \ langle \ hat t_ {ab} {ab}（x）\ rangle_ {rangle_ {ren} $，已经在分布量field-indmimum field in n in classion insmumum field nories。结果表明，即使将这些空间时间放大以包括大爆炸（或大键），它们也可以作为定义明确的分布扩展。我们将这些结果推广到空间闭合和开放的FLRW模型，表明这种宇宙学奇异性的“驯服”并不是由于空间平坦度而导致的技术简化的工件。我们的分析还提供了$ \ langle \ hat ϕ（x）\ hat ϕ（x'）\ rangle_ {ren} $，$ \ langle \ hat ϕ（x）^2 \ rangle_ {rangle_ {ren} $和$ \ langle \ hat t_ t_ ab {ab}（ab and iniim iniim and coolly）的明确表达式。耦合了无质量标量字段，并讨论了$ \ langle \ hat t_ {ab}（x）（x）\ rangle_ {ren} $的定义中的歧义。尽管技术表达比在空间平坦的情况下更为复杂，但也存在一个意外的概念简化：现在不存在红外差异\ cite {fp}，因为实际上，空间曲率提供了自然的截止。最后，我们进一步阐明了量子场理论可以继续得到充分定义的意义，即使扩展的时空由于奇异性而不是全球双曲线，并提出了进一步工作的方向。
It was recently pointed out that linear quantum fields $\hat ϕ(x)$ can be meaningfully propagated across the big bang (and the big crunch) singularities of spatially flat Friedmann, Lemaître, Robertson, Walker (FLRW) universes \cite{ADLS2021}. Recall that $\hat ϕ(x)$, as well as renormalized observables $\langle\hat ϕ(x)^2 \rangle_{ren}$ and $\langle \hat T_{ab}(x)\rangle_{ren}$, are distribution-valued already in Minkowskian quantum field theories. It was shown that they can be extended as well-defined distributions even when these space-times are enlarged to include the big-bang (or the big crunch). We generalize these results to spatially closed and open FLRW models, showing that this `tameness' of cosmological singularities is not an artifact of the technical simplifications due to spatial flatness. Our analysis also provides explicit expressions of $\langle\hat ϕ(x) \hat ϕ(x') \rangle_{ren}$, $\langle\hat ϕ(x)^2 \rangle_{ren}$ and $\langle \hat T_{ab}(x)\rangle_{ren}$ in closed and open universes for minimally coupled massless scalar fields and discuss the ambiguities in the definition of $\langle \hat T_{ab}(x)\rangle_{ren}$ at the big-bang. While the technical expressions are more complicated than in the spatially flat case, there is also an unexpected conceptual simplification: the infrared divergence \cite{fp} is now absent because, in effect, the spatial curvature provides a natural cutoff. Finally, we further clarify the sense in which quantum field theory can continue to be well defined even though the extended space-time is not globally hyperbolic because of the singularity, and suggest directions for further work.
