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#### Probing the Big Bang with quantum fields

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##### Citation

Ashtekar, A., De Lorenzo, T., & Schneider, M. (2021). Probing the Big Bang with
quantum fields.* Advances in theoretical and mathematical physics,* *25*(7),
1651-1702. doi:10.4310/ATMP.2021.v25.n7.a1.

Cite as: https://hdl.handle.net/21.11116/0000-0008-E44B-3

##### 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.

$\hat{\phi}(x)$ 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.