Casertano et al. have used Gaia to provide a small but important update in the debate over the value of the Hubble Constant. The ESA Gaia mission is measuring parallaxes for billions of stars. This is fundamental data that will advance astronomy in many ways, no doubt settling long standing problems but also raising new ones – or complicating existing ones.

Traditional measurements of the H_{0} are built on the distance scale ladder, in which distances to nearby objects are used to bootstrap outwards to more distant ones. This works, but is also an invitation to the propagation of error. A mistake in the first step affects all others. This is a long-standing problem that informs the assumption that the tension between H_{0} = 67 km/s/Mpc from Planck and H_{0} = 73 km/s/Mpc from local measurements will be resolved by some systematic error – presumably in the calibration of the distance ladder.

Well, not so far. Gaia has now measured enough Cepheids in our own Milky Way to test the calibration used to measure the distances of external galaxies via Cepheids. This was one of the shaky steps where things seemed most likely to go off. But no – the scales are consistent at the 0.3% level. For now, direct measurement of the expansion rate remains H_{0} = 73 km/s/Mpc.

So, what would happen to the Standard Model of Cosmology if one assumed that the Planck measure is wrong and we used 73 km/s/Mpc as the value for H0? What problem(s) would this cause?

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Good question. I wish it had a good answer.

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In thinking about the Hubble Constant, I started thinking about the measurement of redshift and what it actually represents.

It appears to consist of two elements:

1. The redshift of light measures the integrated metric expansion of space as light travels from source to earth based detector. This is the continuous expansion of the “metric frame” in which light moves, gradually stretching its wavelength over time. As far as I understand it, most of the observed redshift arises from this cause.

2. There are also small redshift or blue-shift changes that ride on the main red-shift signal, due to something like earth bound “Doppler shifts”; this must be true otherwise we would not see galactic rotation curves and Doppler shifts in the Cosmic background radiation due to the earths rotation around the sun, plus the sun’s rotation around the galaxy etc.

Despite needing General Relativity to account for cause 1, it is cause 2 that causes most confusion for me and perhaps others. Conventional Doppler shifts just require a relative velocity difference between the light source and the detector. The speed of light itself does not change, just the wavelength and frequency of light change in inverse proportion.

However a “Doppler shift” across expanding space is not so simple. If you needed to include the relative velocity between source and detector at the time when a light signal was emitted (something we can’t measure directly), plus the metric expansion redshift due to cause 1, it seems to me that you would always end up with the same redshift measurement for all stellar objects in the sky. Clearly wrong.

Therefore it seems that the already existing difference in relative velocity between two simultaneous and distant “cosmological frames of rest” (e.g. our local CMBR rest frame) when light is emitted from a source does not form part of the eventual “Doppler shift” element of the redshift measurement.

This may mean that acceleration is the important explanatory attribute of cause 2, not relative velocity, as with a conventional Doppler shift within the same local cosmological frame of rest.

On a related point. Researchers at University of Oxford have begun to question the accelerated expansion of the universe

http://www.ox.ac.uk/news/science-blog/universe-expanding-accelerating-rate-%E2%80%93-or-it

In defence of the accelerated expansion I have found this paper on the pre-print archive

https://arxiv.org/ftp/arxiv/papers/1611/1611.00999.pdf

See Figure 2 of this paper – scale factor vs. cosmological time (t=1 be the present time) – which is supposedly conclusive proof for an accelerated universe.

However I think that in the early universe we may be measuring the titanic struggle between the uniform expansion of space and the accelerated gravitational collapse of material on various distance and time scales, with the expansion of space eventually winning out. If this is true then the “noise” in the data will only get larger the further back in time we view (still with no data points under the straight line “Milne Curve” given in figure 2.) In that case the CMBR is effectively an early data point in figure 2 with redshift “noise” distributed over all distance scales. This conclusion is conjectural and incompatible with the LCDM curve in figure 2 and the associated standard model of cosmology interpretation.

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Needless to say I made some silly obvious mistakes in my comments above.

Rather than try again and make more mistakes – If you are sceptical about Dark Energy and worried about the tension in the various Hubble constant determinations, a relevant paper is

https://arxiv.org/pdf/1607.08797.pdf

“Concordance cosmology without dark energy”

I think it links up with what I was unsuccessfully trying to say.

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Hi, There is now a very simple way to calculate Hubble’s Constant, by inputting to an equation, the numerical value of Pi and the speed of light (C) from Maxwell’s equations. NO space probe measurements (with their inevitable small measuring / interpretation errors) are now required. Hubble’s Constant is ‘fixed’ at 70.98047 PRECISELY. This maths method removes the errors / tolerances that is always a part of attempting to measuring something as ‘elusive’ as Hubble’s Constant.

The equation to perform this can be found in ‘The Principle of Astrogeometry’ on Amazon Kindle Books, David.

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