Utilizing a newly revealed symmetry of observables with fundamental constant variation to resolve the Hubble Tension.*

The tension between local and distant measurements of H₀ continues without resolution. It was recently pointed out that cosmic microwave background (CMB) and large-scale structure (LSS) observables are invariant under a uniform rescaling of the gravitational free-fall rates of all species present and the Thomson scattering rate between photons and electrons. We show here that a specific variation of the fine-structure constant and the electron mass can exploit this scaling transformation to make the CMB and LSS data compatible with a broad range of Hubble constant values, including those inferred from local measurements. Our work highlights the importance of the Thomson scattering rate to the current Hubble tension and provides a clear target for particle model builders.