Validity Domains for Semiclassical Time in Quantum Cosmology
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.
Versions
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BibTeX
@misc{rosati2026validity,
title = {{Validity Domains for Semiclassical Time in Quantum Cosmology}},
author = {Gianpaolo Rosati and Sergio L. Cacciatori},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37696},
eprint = {2610.37696},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37696},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Validity Domains for Semiclassical Time in Quantum Cosmology
AU - Gianpaolo Rosati
AU - Sergio L. Cacciatori
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.37696
UR - https://arxiv.org/abs/2610.37696
AB - 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 D_t = D_WKB ∩ D_ad ∩ D_sharp, 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.
ER -