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

We find that a uniform scaling of the gravitational free-fall rates and photon-electron scattering rate leaves most dimensionless cosmological observables nearly invariant. This result opens up a new approach to reconciling cosmic microwave background and large-scale structure observations with high values of the Hubble constant H0: Find a cosmological model in which the scaling transformation can be realized without violating any measurements of quantities not protected by the symmetry. A ???mirror world??? dark sector allows for effective scaling of the gravitational free-fall rates while respecting the measured mean photon density today. Further model building might bring consistency with the two constraints not yet satisfied: the inferred primordial abundances of deuterium and helium.