The background Friedmannian Hubble constant in relativistic
  inhomogeneous cosmology and the age of the Universe
  In relativistic inhomogeneous cosmology, structure formation couples to
average cosmological expansion. A conservative approach to modelling this
assumes an Einstein--de Sitter model (EdS) at early times and extrapolates this
forward in cosmological time as a "background model" against which average
properties of today's Universe can be measured. This requires adopting an
early-epoch--normalised background Hubble constant $H_1^{bg}$. Here, we show
that the $\Lambda$CDM model can be used as an observational proxy to estimate
$H_1^{bg}$ rather than choose it arbitrarily. We assume (i) an EdS model at
early times; (ii) a zero dark energy parameter; (iii) bi-domain scalar
averaging---division of the spatial sections into over- and underdense regions;
and (iv) virialisation (stable clustering) of collapsed regions. We find
$H_1^{bg}= 37.7 \pm 0.4$ km/s/Mpc (random error only) based on a Planck
$\Lambda$CDM observational proxy. Moreover, since the scalar-averaged expansion
rate is expected to exceed the (extrapolated) background expansion rate, the
expected age of the Universe should be much less than $2/(3 H_1^{bg}) = 17.3$
Gyr. The maximum stellar age of Galactic Bulge microlensed low-mass stars (most
likely: 14.7 Gyr; 68\% confidence: 14.0--15.0 Gyr) suggests an age about a Gyr
older than the (no-backreaction) $\Lambda$CDM estimate.
