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Riess and Plancks Hubble constant values

Just an update for anyone interested…

Continuing from this https://forum.cosmoquest.org/showthr...how&highlight=

In a previous post https://forum.cosmoquest.org/showthr...pc)&highlight= it was argued that the rate of expansion of the universe is half of Hubbles constant i.e a(dot)/a is approximately 36km/s/Mpc

It was argued that this was due to a misunderstanding of the redshift-scalefactor relation which should really be 1+z = [a(0)/a(1)]^2

Which in turn led to a luminosity distance dL=(2c/H(0))*(1+z)sqrt[(1+z)-1] and an apparent omega(m) of exactly 0.25 from CMB, and just under 1/3 from supernovae

... this graph https://www.desmos.com/calculator/njz3vohptp (Betoule data) shows that the above equation, matches supernovae data well, with constant H(0), i.e. q(0)=-1 (constant). The top orange curve is the above equation, the middle green one is LCDM with omega(m)=0.3089 and the bottom is CDM with omega(m)=1

Consistency can be found from Riess and Planck data as follows…

1) Planck https://arxiv.org/abs/1502.01589 uses BAO data to determine H(0)

section 5.2 formula (25), has the expression cz/H, in which the z should be 2[sqrt(1+z)-1]

A z of 0.57 is used, so BAO might overestimate distances by a factor 1.126 (0.57 compared to 0.505993) and hence underestimate Hubbles constant by the same factor.

Plancks value of 67.3km/s/Mpc, formula (27), times by 1.126 becomes 75.8 km/s/Mpc.

2) With omega(m) as 0.25 and using the latest Planck value for omega(m)h^2 of 0.142 gives H(0) = 75.4km/s/Mpc

3) Riess 2016 https://arxiv.org/abs/1604.01424 has H(0) of 73.24, but in the analysis uses q(0)=-0.55 derived (as mentioned near the bottom of page 15) from his 2007 paper, which uses the assumption of the faulty LCDM model. The q(0) should be -1.

When this value is applied to equation (5) it changes ax and so from equation (4) changes H(0), by a factor 10^ax. The data has redshift between 0.023 and 0.15, with more data near the 0.15 side, figure 8 page 47. The change at different redshifts is: for z=0.023 it's by a factor 1.0052, z=0.05 it’s 1.01115, z=0.1 it's 1.0235, z=0.15 it's 1.036 so a factor 1.025 is applied. 73.24*1.025 = 75.1km/s/Mpc

1-3) are consistent with each other given the errors involved and have an average value of about 75.4km/s/Mpc

Last edited by john hunter; 2018-Jan-07 at 11:12 PM.

...when you have eliminated the impossible, whatever remains, however improbable, must be the truth. Sherlock Holmes