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I am writing an equation using the Hubble constant. My work is based on Dodelson's article on sterile neutrinos which uses a C$+$HDM model.In it a value of $h=0.5$.

But when reading the more recent Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Observations: Implications for Cosmology, which uses a $\Lambda$CDM model, a value of $h=0.732$ is used.

Is this because this last article is more recent and the value has been measured more accurately? Or is it because they are different models and therefore I should use the Hubble constant that fits my model?

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The Wikipedia article on Hubble's law says

Hubble's law is considered a fundamental relation between recessional velocity and distance. However, the relation between recessional velocity and redshift depends on the cosmological model adopted and is not established except for small redshifts.

The article also contains a table with a history of estimates of Hubble's constant. Although estimates since 2002 (basically since Hubble space telescope data became available) have been in the region of $70$ km/s/Mpc (corresponding to a $h$ value of $0.7$), earlier estimates ranged from $50$ to $90$ km/s/Mpc. The paper you referenced was published in 1994, so it was pre-Hubble. It is likely that it was simply using an older estimate, which we now know to have been inaccurate.

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