## The background Friedmannian Hubble constant in relativistic inhomogeneous cosmology and the age of the Universe

Context. 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. Aims: This modelling requires adopting an early-epoch-normalised background Hubble constant . Methods: Here, we show that the ΛCDM model can be used as an observational proxy to estimate 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. Results: We find km s-1/ Mpc (random error only) based on a Planck ΛCDM observational proxy. Conclusions: 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 younger than 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 of about a Gyr older than the (no-backreaction) ΛCDM estimate.