How is "little $h$" measured in cosmology? The dimensionless parameter from the Hubble constant, $H_0$
The little $h$ is a historical artifact, one that will probably die out soon enough.
The thing is, $H_0$ was extremely difficult to measure precisely for many decades after its importance was realized. At some point, cosmologists were divided between the "$H_0 = 50\ \mathrm{km/s/Mpc}$" and the "$H_0 = 100\ \mathrm{km/s/Mpc}$" camps. Because the quantity appears as an overall scale factor to some power in many cosmological formulas, people adopted $h$ to be $H_0/(100\ \mathrm{km/s/Mpc})$ by definition. Rather than plugging in their preferred value of $H_0$, they quoted formulas in terms of $h$ and its powers, so that others using different values of $H_0$ could compare to them. All $h$ does is make undoing someone's erroneous value for $H_0$ easier (sort of).
Today, we know $H_0$ to a few percent or so, and few people lose sleep over the imprecision. Since there is nothing physically meaningful about the $100\ \mathrm{km/s/Mpc}$ scaling, it is $H_0$, not $h$, that is more fundamental.
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ShanZhengYang
Updated on August 01, 2022Comments

ShanZhengYang 5 months
Hubble's law has been wellknow for close to a century now. It is written as
$v = H_0 d$
where the Hubble constant $H_0$ is the constant of proportionality between recession speed $v$ and distance $d$ in the expanding Universe.
The expression for the Hubble constant itself is normally written as
$H_0 = 100\,h\,{\rm km}\,{\rm s}^{−1}\,{\rm Mpc}^{−1}$
where $h$ is the dimensionless parameter expressing of ignorance. How is this "little h" measured?
Do astronomers measure the Hubble constant (using Cepheid distances, Type Ia Supernovae, etc.) and then calculate $h$?
Supposedly the value agreed upon today is around $h\approx0.7$. Give or take.

Kyle Kanos over 7 yearsNote that $H_0h=100\cdot0.70=70\,\rm km/s/Mpc$ which is the one of the accepted values of Hubble constant, then extrapolate the definition/meaning of $h$.

KidElephant over 7 yearsWhy should $h$ be measured, when we can instead measure $H_0$ and use the above definition? $H_0$ has physical meaning; $h$ is a shorthand.

Kyle Kanos over 7 yearsI wrote $H_0$ but it should just be the 100, sorry for confusion.


ShanZhengYang over 7 yearsAh, so "little h" is basically just a historical artifact at this point. This answers my question: today, we try to measure $H_0$ and then extrapolate from there. The Hubble constant $H_0$ has been measured fairly precisely. For a recent paper, read Efstathiou, 2014, arXiv:1311.3461v2 Planck (2013) measures $H_0 = 67.3 \pm 1.2 km s^{1} Mpc^{1}$, while direct measurements of Cepheid data comes up with $H_0 = 72.5 \pm 2.5 km s^{1} Mpc^{1}$.

ShanZhengYang over 7 yearsCould you actually provide some more information as to when/why people started using "little h"? It would be good extra historical background.

Kyle Oman over 7 yearsWas about to ask this question as I would have killed for a googleable answer to it when I was a fledgeling student, and came across this. Recent too, I guess I was a little bit too slow. Anyway, I took the liberty of editing in a link to a paper of immense use (imho). The "little h" rabbit hole is deeper than I could have guessed...

pela over 7 years@KyleOman: I was just about to link to that very important paper when I was your comment. :)

Winther over 7 yearsThe rumours of little $h$'s death is greatly exagerated:) The use of $h$ is so ingrained in cosmology that I expect it to be with us long after we hit subpercent accuracy. The value is also model dependent so as long as there exist viable alternatives to $\Lambda$CDM it will stick around. I bet it has at least $50$ more years left.