Solving the Hubble tension à la Ellis & Stoeger 1987

Abstract: The discrepancy between the value of the Hubble constant $H_0$ in the late, local universe and the one obtained from the Planck collaboration representing an all-sky value for the early universe reached the 5-$\sigma$ level. Approaches to alleviate the tension contain a wide range of ansatzes: increasing uncertainties in data acquisition, reducing biases in the astrophysical models that underly the probes, or taking into account observer-dependent variances in the parameters of the cosmological background model. Yet, early and late universe probes are often treated as independent, they live on different length scales, and require different perturbations to be subtracted. Hence, fitting a flat Friedmann-Lema^itre-Robertson-Walker cosmology to different probes at different cosmic epochs can yield different sets of cosmological parameter values. Tensions arise if these background fits and perturbing biases are not consistently calibrated or synchronised with respect to each other. This consistent model-fitting calibration is lacking between the two $H_0$ values mentioned above, thus causing a tension. As shown here, this interpretation resolves the $H_0$tension, if 15% of the matter-density parameter obtained from the fit to the cosmic microwave background, $\Omega_m = 0.315$, are assigned to decoupled perturbations yielding $\Omega_m = 0.267$ for the fit at redshifts of the supernova observations. Existing theoretical analyses and data evaluations which support this solution are given.