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

¹ Toruń Centre for Astronomy, Faculty of Physics, Astronomy and Informatics, Grudziadzka 5, Nicolaus Copernicus University, ul. Gagarina 11, 87-100 Toruń, Poland
e-mail: boud@astro.uni.torun.pl
² Univ. Lyon, Ens de Lyon, Univ. Lyon1, CNRS, Centre de Recherche Astrophysique de Lyon UMR 5574, 69007 Lyon, France
³ Département de Physique, École normale supérieure, 24 rue Lhomond, 75230 Paris Cedex 05, France

Received: 9 October 2016
Accepted: 27 November 2016

Abstract

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^bg₁.

Methods. Here, we show that the ΛCDM model can be used as an observational proxy to estimate H^bg₁ 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^bg₁= 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/(3H^bg₁) = 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.