Probing the Big Bang with quantum fields

Abstract

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 $⟨\hat{\varphi }(x)\hat{\varphi }(x^{\prime })⟩$ 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 $⟨{\hat{\varphi }}^2(x){⟩}_{\mathrm{ren}}$ and $⟨{\hat{T}}_{ab}(x){⟩}_{\mathrm{ren}}$ 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.

38 pages; Three small clarifications added and minor typos corrected. Version to appear in Advances in Mathematical and Theoretical Physics

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• Hamiltonian General Relativity and the Belinskii, Khalatnikov, Lifshitz Conjecture
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