Geometric Interpretation of the Redshift Evolution of H_0(z)

TL;DR

This paper proposes a geometric interpretation for the observed redshift dependence of the Hubble constant, attributing it to a gauge-dependent normalization of cosmic time rather than new physics, thus offering a unified explanation for the Hubble tension.

Contribution

It introduces a geometric framework that explains the redshift evolution of H_0(z) and SN Ia light-curve variations through time-normalization, avoiding modifications to cosmic expansion.

Findings

Redshift dependence of H_0(z) can be explained by gauge-dependent time normalization.

The geometric interpretation unifies Hubble tension and SN Ia observations.

Background distances remain unchanged under the proposed normalization.

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)^{-\alpha}, where \alpha quantifies 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.