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

TL;DR

This paper estimates the background Hubble constant in inhomogeneous cosmology using a mbda CDM proxy, finding it to be around 37.7 km/s/Mpc, and discusses implications for the Universe's age based on stellar ages.

Contribution

It introduces a method to estimate the background Hubble constant in inhomogeneous cosmology models using mbda CDM as an observational proxy.

Findings

Estimated background Hubble constant: 37.7 km/s/Mpc.

The Universe's age is likely less than 17.3 Gyr.

Stellar ages suggest an older Universe than standard mbda CDM estimates.

Abstract

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.