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Register a new userLimits on the global Hubble constant and the age of the universe
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While the recent discovery of the Cepheid variables in the Virgo cluster galaxies puts additional support for the Hubble constant $H_0 sim 80$km/sec/Mpc, a relatively lower value $H_0 sim 50$km/sec/Mpc is suggested by other distance indicators based on the Sunyaev-Zeldovich effect and the gravitational lens which probe the universe at higher redshifts $z=(0.1sim 1)$. In order to reconcile the possible discrepancy between the estimates of the Hubble constants from nearby galaxy samples and high-redshift clusters, we consider a model of locally open universe embedded in the spatially flat universe. We find analytic expressions for the lower limit on the global Hubble constant $hg$, and the upper limit on the age of the universe with a given value for the Hubble constant $hl$ in the local universe. We conclude that it is quite unlikely that the above difference in the estimates of the Hubble constant is explained within the framework of the gravitational instability picture.
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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 todays 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.
I review the current state of determinations of the Hubble constant, which gives the length scale of the Universe by relating the expansion velocity of objects to their distance. There are two broad categories of measurements. The first uses individual astrophysical objects which have some property that allows their intrinsic luminosity or size to be determined, or allows the determination of their distance by geometric means. The second category comprises the use of all-sky cosmic microwave background, or correlations between large samples of galaxies, to determine information about the geometry of the Universe and hence the Hubble constant, typically in a combination with other cosmological parameters. Many, but not all, object-based measurements give $H_0$ values of around 72-74km/s/Mpc , with typical errors of 2-3km/s/Mpc. This is in mild discrepancy with CMB-based measurements, in particular those from the Planck satellite, which give values of 67-68km/s/Mpc and typical errors of 1-2km/s/Mpc. The size of the remaining systematics indicate that accuracy rather than precision is the remaining problem in a good determination of the Hubble constant. Whether a discrepancy exists, and whether new physics is needed to resolve it, depends on details of the systematics of the object-based methods, and also on the assumptions about other cosmological parameters and which datasets are combined in the case of the all-sky methods.
For precision cosmological studies it is important to know the local properties of the reference point from which we observe the Universe. Particularly for the determination of the Hubble constant with low-redshift distance indicators, the values observed depend on the average matter density within the distance range covered. Here we used the spatial distribution of galaxy clusters to map the matter density distribution. The study is based on our CLASSIX galaxy cluster survey, which is highly complete and well characterised with galaxy clusters detected in X-rays. We find a local underdensity in the cluster distribution of about 30 - 60% which extends ~85 Mpc to the north and ~170 Mpc to the south. For three regions for which the galaxy density distribution has previously been studied, we find good agreement between the density distribution of clusters and galaxies. Correcting for the bias in the cluster distribution we infer an underdensity in the matter distribution of about -0.3 +- 0.15 (-0.2 +- 0.1) in a region with a radius of about 100 (~140) Mpc. Calculating the probability of finding such an underdensity theoretically in a LambdaCDM universe with concordance cosmological parameters, we find a probability characterised by sigma-values of 1.3-3.7. This indicates low probabilities, but with values of around 10% at the lower uncertainty limit, the existence of an underdensity cannot be ruled out. Inside this underdensity, the observed Hubble parameter will be larger by about 5.5 +2.1-2.8%, which explains part of the discrepancy between the locally measured value of H_0 compared to the value of H_0 inferred from the Planck observations of cosmic microwave background anisotropies. If distance indicators outside the local underdensity are included, as in many modern analyses, this effect is diluted.
A brief history of the determination of the Hubble constant H_0 is given. Early attempts following Lemaitre (1927) gave much too high values due to errors of the magnitude scale, Malmquist bias and calibration problems. By 1962 most authors agreed that 75< H_0 <130. After 1975 a dichotomy arose with values near 100 and others around 55. The former came from apparent-magnitude-limited samples and were affected by Malmquist bias. New distance indicators were introduced; they were sometimes claimed to yield high values of H_0, but the most recent data lead to H_0 in the 60s, yet with remaining difficulties as to the zero-point of the respective distance indicators. SNe Ia with their large range and very small luminosity dispersion (avoiding Malmquist bias) offer a unique opportunity to determine the large-scale value of H_0. Their maximum luminosity can be well calibrated from 10 SNe Ia in local parent galaxies whose Cepheids have been observed with HST. An unforeseen difficulty - affecting all Cepheid distances - is that their P-L relation varies from galaxy to galaxy, presumably in function of metallicity. A proposed solution is summarized here. The conclusion is that H_0 = 63.2 +/- 1.3 (random) +/- 5.3 (systematic) on all scales. The expansion age becomes then (with Omega_m=0.3, Omega_Lambda=0.7) 15.1 Gyr.
Dark energy is inferred from a Hubble expansion which is slower at epochs which are earlier than ours. But evidence reviewed here shows $H_0$ for nearby galaxies is actually less than currently adopted and would instead require {it deceleration} to reach the current value. Distances of Cepheid variables in galaxies in the Local Supercluster have been measured by the Hubble Space Telescope and it is argued here that they require a low value of $H_0$ along with redshifts which are at least partly intrinsic. The intrinsic component is hypothesized to be a result of the particle masses increasing with time. The same considerations apply to Dark Matter. But with particle masses growing with time, the condensation from plasmoid to proto galaxy not only does away with the need for unseen ``dark matter but also explains the intrinsic (non-velocity) redshifts of younger matter.
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