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arXiv · 1608.06004

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

Boudewijn F. Roukema·Pierre Mourier·Thomas Buchert·Jan J. Ostrowski
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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.

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Boudewijn F. Roukema, Pierre Mourier, Thomas Buchert, Jan J. Ostrowski. 2016-08-21. The background Friedmannian Hubble constant in relativistic inhomogeneous cosmology and the age of the Universe. https://doi.org/10.1051/0004-6361/201629868

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