A Symmetry of the Cosmological Observables, a Mirror World Dark Sector and the Hubble Constant Tension*

We point out a way to make large changes in cosmological parameters while preserving consistency with measurements of CMB temperature and polarization, relative luminosity distances, and many large-scale structure observables. These large changes are possible due to a previously unnoticed scaling transformation symmetry. Under the assumption of equilibrium recombination, the scaling symmetry is exact under uniform scaling of the photon scattering time scale and the gravitational time scales. The scaling transformation of the gravitational time scales is severely constrained by the FIRAS measurement of the mean density of the CMB today. To circumvent this constraint we use a "mirror world" dark sector which is a dark copy of the photons, baryons, and neutrinos in our model. To enforce the scaling of the photon scattering rate, we alter the primordial helium abundance. Due to the sensitivity to the reaction rates of non-equilibrium evolution, the recombination and big bang nucleosynthesis can break the symmetry. We find the non-equilibrium recombination only very mildly breaks the symmetry while the primordial helium and deuterium abundance measurements place strong constraints on the model. We thus have re-mapped the problem of reconciling a higher H0 with thousands of data points to one of reconciling it with only two. Our work motivates more research for detailed dark sector particle physics models and an observationally-viable way to achieve a higher photon scattering rate.