# Hubble constant, Riess and why has $q_0 = -0.55$ been used?

Lot's of scientists, including Riess, have done great work in trying to determine the Hubble constant, both from observation and theory. As everyone will know there still exists the problem with the Hubble tension.

Adam Riess and his team have published a value of 74.03km/s/Mpc [2019] for the Hubble constant (Concordance cosmology has a lower 67.3). Looking into this you have to go to the 2016 paper https://arxiv.org/abs/1604.01424 and the 74.03 value is proportional to the quantity (eqn 5, page 15)

$$a_x = 1+\frac{1}{2}\left(1-q_0\right)z-\frac{1}{6}\left(1-q_0-3q_0^2+j_0\right)z^2$$

and a few lines after this equation is this sentence

"Together with the present acceleration $$q_0 = −0.55$$ and prior deceleration $$j_0 = 1$$ which can be measured via high-redshift SNe Ia..."

The question is, why has this value been used? Isn't it dangerous, after all the careful work, to use a value that depends on high redshift supernovae - seemingly making the method rely on other cosmological assumptions and spoiling the 'local method'?

Here is some work on the answer so far:

On page 47, Figure 8, they have a fit against data between redshift 0.0233 and 0.15 and the -0.55 number is obtained from that, but doesn't it still make assumptions about the cosmological model?

The high value seems fine (compared to 67km/s/Mpc), Riess has done great work - but maybe it should be even higher. An estimated reworking with $$q_0=-1$$ gives about 75km/s/Mpc and to avoid spoiling the conclusion, wouldn't it have been better to also publish a graph showing how the value varies with different assumptions about $$q_0$$?

• Please take a look at arxiv.org/pdf/1907.04869.pdf Page 13 Figure 4. The Hubble tension is based on some results a few years old now that depended on assuming the universe is flat. Figure 4 shows some more recent results based on assuming the universe is finite and curved.
– Buzz
Jun 8, 2021 at 20:35
• The same sentence says " which can be measured via high-redshift SNe Ia (Riess et al. 2007; Betoule et al. 2014) independently of the CMB or BAO". This implies it doesn't depend on the cosmological model, no? Jun 10, 2021 at 2:02
• but using high redshift supernovae incorporates possibly faulty assumptions about how luminosity distance relates to redshift - this same supernovae data is used to conclude an accelerating universe and dark energy, so indirectly a model is assumed. The assumption of $a=\frac{1}{1+z}$ is assumed by the supernovae data, but may not be valid , physics.stackexchange.com/questions/638673/… and physics.stackexchange.com/questions/620794/… Jun 10, 2021 at 13:21