Inaccessibility of the Cosmological Singularity to Quantum Probes

Abstract

We propose an operational resolution of the FLRW big bang singularity using quantum probes satisfying a curvature coupled Klein-Gordon equation. Applying the Madelung-Bohm decomposition of a Klein-Gordon field on a classical near-singularity FLRW background, we show that the induced conformal geometry renders curvature invariants finite and makes past directed causal geodesics complete. The classical big bang surface is therefore inaccessible to this class of quantum probes in finite effective proper time, while the underlying FLRW spacetime remains singular.