Casting the $H_0$ tension as a fitting problem of cosmologies
  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. Another way of interpreting the tension is to consider the density
parameters in the Friedmann equations effective background fields which are
probed at two different cosmic times, i.e. using the data of the early universe
and the late, more complex universe for two different fits of a flat
Friedmann-Lema\^itre-Robertson-Walker cosmology. The two sets of parameter
values can differ and tensions arise if these background fits and perturbing
biases are not consistently calibrated with respect to each other when they are
linked to observables because these observables are all based on common
standards. 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,
$\Omega_\mathrm{m}=0.315$, are assigned to decoupled perturbations yielding
$\Omega_\mathrm{m}=0.267$ for the fit at redshifts of the supernova
observations. Existing theoretical analyses and data evaluations which support
this solution are given.
