Resolving the Hubble Tension via Time Reparametrization Invariant Scaling Symmetry

Introduction: The persistent discrepancy between local measurements of the Hubble constant (H₀) and those inferred from the Cosmic Microwave Background (CMB)—known as the Hubble Tension—remains a fundamental crisis in modern cosmology. While many attempts to resolve this issue rely on ad hoc models involving exotic fields or novel particles, a powerful guiding principle is needed to narrow the boundless space of possibilities. Recently, Courbin and Maeder (2026) demonstrated that the Scale Invariant Vacuum (SIV) paradigm offers a natural solution.

Methods: This work utilizes Time Reparametrization Invariant Scaling Symmetry (RISS), a framework that is mathematically equivalent, but physically distinct, to SIV. Instead of introducing new physical entities, we consider a time-dependent conformal unit rescaling, (dt, dr) →λ(t)(dt, dr), which maintains a constant speed of light. This transformation is alternatively considered as a Weyl scaling of the scale factor and lapse function, (a, N) → λ(t)(a, N), yielding a self-consistent augmentation of the standard Friedmann–Lemaître–Robertson–Walker (FLRW) equations.

Results: We show that the time-dependent unit rescaling almost exactly matches the modern treatment of CMB physics. The resulting augmented cosmological equations reveal that the observed H₀ tension is an artifact of treating time units as static across cosmic epochs. Because the global gravitational potentials differ significantly between the decoupling era and the current epoch, the effective unit of time has evolved.

Conclusions: Consequently, the H₀ tension is naturally resolved not by changing the intrinsic expansion rate of the universe, but by properly accounting for the conversion of time units between the early and late universe. RISS provides an elegant, symmetry-based solution to a premier cosmological puzzle without invoking dark sectors or exotic physics.