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arXiv · 2609.35903

Revisiting the Duff Argument in Cosmology: From Dimensional Quantities to Cross-Epoch Observables

Seokcheon Lee
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Abstract

The standard Duff-type argument states that the numerical variation of a dimensional constant is unit-dependent when considered in isolation from the physical standards used to compare it, and is therefore not by itself an observable. We ask whether this conclusion is sufficient to determine the observational status of complete relations connecting different cosmological epochs. In a Robertson--Walker spacetime, the cosmological principle and Weyl's postulate fix the homogeneous geometry and fundamental timelike congruence without uniquely fixing the temporal rate along it. The Hamiltonian constraint likewise does not dynamically select that rate. Consequently, Robertson--Walker spacetime admits a family of homogeneous temporal parametrizations. Generalized Cosmological Time retains a specified common member, T_G, related to proper time by d tau = N_G d T_G, with (tau, 1) as the unit-rate special member of the same class. In the minimally extended varying speed of light framework, length--mass--time quantities obey correlated slice-wise scalings chosen to preserve the same local physical laws on every homogeneous hypersurface. These scalings form a unit-rescaling structure, so purely local dimensionless observables are insensitive to N_G. Cross-epoch observables require more than such local scalings. They also require local reference standards, a propagation or comparison map, and, when distinct source populations are compared, a source-equivalence prescription. Cosmological time dilation illustrates this distinction: its interpretation depends on source standardization and residual source evolution. We distinguish the unit dependence of individual dimensional quantities from the observational content of complete cross-epoch relations. The former does not by itself determine the latter.

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Seokcheon Lee. 2026-10-29. Revisiting the Duff Argument in Cosmology: From Dimensional Quantities to Cross-Epoch Observables. https://arxiv.org/abs/2609.35903

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