Temporal Metric Cosmology: A Kinematical Extension of FLRW with Scale-Factor-Dependent Time Normalization

We propose a minimal kinematical extension of the standard FLRW cosmological framework in which the normalization of cosmic time acquires a scale-factor-dependent modification alongside spatial expansion. While local proper time remains invariant by construction and General Relativity is left entirely unmodified, the relation between physical cosmic time and observer time is allowed to vary cosmologically. For clarity, we refer to this framework as Temporal Metric Cosmology (TMC), emphasizing that it represents a kinematical modification of the temporal normalization within the FLRW metric rather than a modification of the gravitational field equations. No additional fields, energy components, or violations of covariance are introduced. The cosmological redshift remains purely geometric, but the inferred expansion history is altered due to the modified temporal normalization.As a result, the Hubble parameter measured by observers differs from the physical expansion rate governing the Friedmann dynamics. A simple toy parametrization, yields an apparent late-time acceleration and naturally alleviates the Hubble tension for β ∼ 0.08 without invoking dark energy. The luminosity-distance relation is modified such that Type Ia supernova data exhibit apparent acceleration even for a decelerating spatial expansion. Local physics and early-universe processes remain unaffected within current observational bounds. We discuss constraints from CMB and BAO distance scales, implications for structure growth, and outline observational tests including redshift drift and standard sirens. This framework suggests that several cosmological tensions attributed to dark energy may instead originatefrom implicit assumptions about the normalization of cosmic time.