By carrying out a systematic investigation of linear, test quantum fields $\hat{\varphi}(x)$ in cosmological space-times, we show that $\hat{\varphi}(x)$ remain well-defined across the big bang as operator valued distributions in a large class of Friedmann, Lemaître, Robertson, Walker space-times, including radiation and dust filled universes. In particular, the expectation values $\hat{\varphi}(x) \langle \hat{\varphi}(x^\prime) \rangle$ are well-defined bi-distributions in the extended space-time in spite of the big bang singularity. Interestingly, correlations between fields evaluated at spatially and temporally separated points exhibit an asymmetry that is reminiscent of the Belinskii, Khalatnikov, Lifshitz behavior. The renormalized products of fields ${\langle \hat{\varphi}^2 (x) \rangle}_{\mathrm{ren}}$ and ${\langle \hat{T}_{ab} (x) \rangle}_{\mathrm{ren}}$ also remain well-defined as distributions. Conformal coupling is not necessary for these considerations to hold. Thus, when probed with observables associated with quantum fields, the big bang (and the big crunch) singularities are quite harmless.

中文翻译：

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用量子场探索大爆炸

通过对宇宙时空中的线性测试量子场 $\hat{\varphi}(x)$ 进行系统研究，我们表明 $\hat{\varphi}(x)$爆炸作为运营商价值的分布在弗里德曼、勒梅特、罗伯逊、沃克的一大类时空中，包括辐射和充满尘埃的宇宙。特别是，期望值 $\hat{\varphi}(x) \langle \hat{\varphi}(x^\prime) \rangle$ 是扩展时空中的定义明确的双向分布，尽管大爆炸奇点。有趣的是，在空间和时间分离的点处评估的场之间的相关性表现出一种不对称性，这让人联想到 Belinskii、Khalatnikov、Lifshitz 的行为。域 ${\langle \hat{\varphi}^2 (x) \rangle}_{\mathrm{ren}}$ 和 ${\langle \hat{T}_{ab} (x) \ 的重整化积rangle}_{\mathrm{ren}}$ 也被定义为分布。为了满足这些考虑，保形耦合不是必需的。因此，当用与量子场相关的可观测物进行探测时，