2026/07/27 by Dimitris Vartziotis
paper · doi:10.1088/1402-4896/ae913f
Abstract Cosmological inference is constructed from clock readings, frequency ratios and signal propagation. In standard FLRW analyses the time coordinate appearing in the metric is implicitly identified with the time realised by physical clocks, so observations are interpreted as reconstructing the corresponding geometric Hubble rate. We show that this identification is an additional physical assumption: observational protocols reconstruct an expansion history defined with respect to the proper time measured by matter. In pure Einstein-Hilbert general relativity, the gravitational and matter metrics coincide, so the conformal mismatch vanishes. A non-zero mismatch field therefore parametrises departures from this standard identification. In any generally covariant framework in which all matter fields—including photons and clocks—are minimally and universally coupled to a single metric g µν , cosmological observables determine an expansion rate defined with respect to the proper time of that metric. For a homogeneous conformal relation between a gravitational-sector metric g µν and the matter metric, g µν = (1 + Φ) -1 g µν , we derive the corresponding operational-geometric FLRW mapping and show that background distance-redshift data constrain only the operational expansion history, equivalently H phys (z). At the homogeneous level there exists an exact degeneracy between the geometric scale factor α(t) and a mismatch field Φ(t) that leaves ã = α / √ (1 + Φ) unchanged. Time-domain probes such as cosmic chronometers and, in particular, redshift drift directly access H phys (z) and therefore provide calibration independent consistency tests of the operational FLRW description. We also clarify the interpretation of a non-zero Φ, its possible dynamical realisations, and the distinction between background kinematics and model-dependent dynamics. We provide an illustrative estimate of the conformal mismatch required to account for the Hubble tension and identify perturbation theory as the next step for assessing the S 8 matter clustering tension.