Resolving the Hubble Tension via a Scaling Factor to Account for the Evolving Gravitational Potential of the Universe

A recent 2026 paper by Courbin and Maeder demonstrated that the Hubble tension can be resolved within the Scale-Invariant Vacuum (SIV) paradigm, but they did not demonstrate that the CMB spectra would be correctly reproduced. In this paper, an equivalent but physically different idea using time Reparameterization-Invariant Scaling Symmetry (RISS) is utilized to build a model that resolves the Hubble tension without introducing new particles or fields. Here, the Hubble tension is recognized to be caused by the difference in the unit of time during the decoupling and the current era since the corresponding gravitational potentials are different. This is justified by considering the SIV-like scaling factor using the Newtonian gauge to define λ=N/N0=(1+2Φ)/N0, where N is the lapse function as related to the evolving gravitational potential Φ and N0 is its current value. Then, by introducing specific λ(a), a new gauge-independent background reformulation is achieved since now λ depends on the expansion scale factor a, which can be viewed as a specific time parametrization for the evolution of the Universe. The key is an epoch-dependent re-scaling of the Hubble function Hnew=ξ(a)−1Hstd(a). Finally, after adjustments to the main cosmology parameters, one can reproduce the original LCDM CMB spectrum within less than a few percent of the individual ClTT values. The values of the new H0 parameter are consistently between H0=70 and 75 km/s/Mpc depending on the adopted model. However, for the RISS/SIV-motivated w=−2/3 extension of the LCDM model, that is, adding 1/a substance, my preliminary MCMC calculations result in H0=72±3 km/s/Mpc, Ωm=0.27, but very high ΩΛ=0.95 and a cosmological fluid with negative energy density Ωw=−0.23.