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Abstract

By carrying out a systematic investigation of linear, test quantum fields
$\hat{\phi}(x)$ in cosmological space-times, we show that $\hat{\phi}(x)$
remain well-defined across the big bang as operator valued distributions in a
large class of Friedmann, Lema\^itre, Robertson, Walker space-times, including
radiation and dust filled universes. In particular, the expectation values
$\langle \hat{\phi}(x)\,\hat{\phi}(x')\rangle$ 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
$\langle \hat{\phi}^2(x)\rangle_{\rm ren}$ and $\langle \hat{T}_{ab}(x)
\rangle_{\rm ren}$ 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.