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 H bg 1 . Methods. Here, we show that the ΛCDM model can be used as an observational proxy to estimate H bg 1 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 H bg 1 = 37.7 ± 0.4 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 2/(3 H bg 1 ) = 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 of about a Gyr older than the (no-backreaction) ΛCDM estimate.