• Accepted Paper

Validity domains for semiclassical time in quantum cosmology

Gianpaolo Rosati and Sergio L. Cacciatori

Phys. Rev. D - Accepted 22 October, 2026

DOI: https://doi.org/10.1103/w7zp-vz6k

Abstract

We investigate the domain in which a semiclassical gravitational WKB flow can serve as a quantitatively controlled temporal reference for subordinate quantum degrees of freedom. Rather than introducing WKB time at the outset, we formulate the Born–Oppenheimer adiabatic condition directly on gravitational configuration space using the Hamilton–Jacobi vector field. This separates adiabatic control from the local WKB validity of the gravitational branch and from the sharpness of the candidate reference against quantum fluctuations. For a single selected semiclassical branch, these requirements define the validity domain Dt = DWKB ∩ Dad ∩ Dsharp, with an additional decoherence condition when coherent branches coexist. In a closed Friedmann–Robertson–Walker minisuperspace coupled to a homogeneous massive scalar mode, the distinction is explicit: approaching the gravitational turning point from the oscillatory region, the ordinary WKB control parameter diverges while the configuration-space adiabatic parameter tends to zero. A uniform Airy treatment of the turning point removes the formal WKB divergence while preserving the inequivalence: the corresponding local control parameter remains of order unity, whereas the configuration-space adiabatic parameter is parametrically suppressed as O(M^{-1/3}). Thus Born–Oppenheimer adiabaticity and gravitational WKB validity define inequivalent domains even within the simplest minisuperspace model. We conclude that the existence of an oscillatory semiclassical branch is not sufficient for a reliable WKB temporal description: semiclassical temporal reliability is instead determined by the overlap of the validity domains supporting the reference flow.

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