Geometric Interpretation of the Redshift Evolution of H_0(z)

TL;DR

The paper tackles the mild redshift evolution observed in locally inferred $H_0$ from SN Ia analyses and proposes a geometric resolution within the Robertson–Walker metric through the meVSL framework. It establishes a direct mapping $\alpha=b/4$ between the empirical exponent $\alpha$ in $\tilde{H}_0(z)=H_0 (1+z)^{-\alpha}$ and a gauge-based lapse parameter $b$, predicting a modified time-dilation law $\tilde{t}_{\rm obs}/\tilde{t}_{\rm emit}=(1+z)^{1-b/4}$ while leaving background distances unchanged. The framework connects SN Ia luminosity calibration, via Chandrasekhar-mass scaling $\tilde{M}_{Ch}\propto a^{-2b}$, to the redshift-dependent magnitude shift $\tilde{\mu}=\mu - 4b\log_{10}(1+z)$, yielding a coherent, single-parameter explanation for the $H_0$ trend without altering expansion dynamics. Current constraints from the Master SN Ia analysis place $b\approx0.04\pm0.02$, compatible with other time-dilation and cosmic-chronometer measurements, and forecast that next-generation surveys will probe $|b|\lesssim 0.01$, offering a falsifiable test of this geometric interpretation and a potential route to reconciling early- and late-Universe measurements of $H_0$ through cosmic time normalization rather than new physics.

Abstract

Recent analyses of the Master Type Ia supernova (SN Ia) sample have revealed a mild redshift dependence in the inferred local Hubble parameter, often expressed as tilde{H}_0(z) = H_0 (1+z)^{-α}, where αquantifies possible departures from the standard cosmological time dilation relation. In this work, we show that such an empirical scaling can be interpreted as a purely geometric effect arising from a small, gauge-dependent normalization of cosmic time within the Robertson-Walker metric. This interpretation naturally unifies the observed redshift evolution of tilde{H}_0(z) and the corresponding deviation in SN Ia light-curve durations under a single geometric time-normalization framework. We demonstrate that this mapping leaves all background distances--linked to the Hubble radius in the general-relativistic frame--unchanged, while the apparent evolution in SN Ia luminosity distances arises from the redshift dependence of the Chandrasekhar mass. The result provides a unified and observationally consistent explanation of the mild Hubble-tension trend as a manifestation of the geometric structure of cosmic time rather than a modification of the expansion dynamics.