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The awkward expression 1 km/s per Mpc--the radius is better
It's been pointed out that by historical accident we've been stuck with an awkward mix of units conventionally used to express Hubble parameter. If you parse the quantities km/s per Mpc you find that the length units cancel and you end up with the reciprocal of time.
So let's take one over the unit and see what time quantity it amounts to.
Go to google and type or paste this in:
1/(1 km/s per Mpc)
Of course you get a time, because the Hubble parameter unit is a reciprocal time in disguise, but it comes out in seconds!
However you can force the google calculator to give the quantity to you in years, simply by adding the words "in years" to what you paste into the window:
1/(1 km/s per Mpc) in years
Google will immediately give you: 977.8 billion years.
So that is what the unit boils down to: (km/s per Mpc) = (977.8 billion years)-1
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But in most of the quantitative cosmology stuff we do around this forum we don't use parsecs and Megaparsecs very much, and recession speed are rarely expressed in km/s. So both those units are rather foreign to the discussion.
The problem, then, is to get the all-important Hubble parameter into some handier form for our purposes.
All things considered, I think the most user-friendly, in particular beginner-friendly, is the conventional Hubble radius. At any given stage in history, the Hubble radius is the distance that is expanding at speed c. So, because of the basic v = H D law, in whatever units you work in it is always true that c = H R and so the Hubble radius R = c/H.
Therefore, if somebody tells you that the Hubble parameter is, say, 67.8 km/s per Mpc,
all you have to do is paste this verbatim into google:
c/(67.8 km/s per Mpc)
and you will get out a certain distance. But it will be in meters! So to force google to tell you the Hubble radius in light years you simply add the words "in light years" to what you paste in:
c/(67.8 km/s per Mpc) in light years
Then google will give you 14.4 billion lightyears.
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That is easy to interpret as a percentage distance growth rate namely 1/144 percent per million years. You can always do that with the Hubble radius if you want to explain it to someone as a percentage growth rate.
And it also means that a sample distance of 1 Gly is growing at a speed of 1/14.4 c, that is slightly less than 1/14 of the speed of light. All the other growth speeds are proportional, so that is also a good way to picture it.
In the standard LCDM model, at any given time, all the cosmological distances (i.e. between pairs of CMB stationary observers) are growing at the same percentage rate, and what seems to be the most user-friendly way to package that information is in the form of the Hubble radius.
=======================
If you look at one of Jorrie's tables you can see what the Hubble radius has been in the past and what it is projected to be in the future. It has been increasing throughout history and is slated to continue increasing (but more and more gradually). So as it increases from the present 14.4 billion LY to, say, a future 17.3 billion LY, you can see that the percentage rate will decline from 1/144 to 1/173 percent per million years. You can always read off the percent rate from the Hubble radius.
It's been pointed out that by historical accident we've been stuck with an awkward mix of units conventionally used to express Hubble parameter. If you parse the quantities km/s per Mpc you find that the length units cancel and you end up with the reciprocal of time.
So let's take one over the unit and see what time quantity it amounts to.
Go to google and type or paste this in:
1/(1 km/s per Mpc)
Of course you get a time, because the Hubble parameter unit is a reciprocal time in disguise, but it comes out in seconds!
However you can force the google calculator to give the quantity to you in years, simply by adding the words "in years" to what you paste into the window:
1/(1 km/s per Mpc) in years
Google will immediately give you: 977.8 billion years.
So that is what the unit boils down to: (km/s per Mpc) = (977.8 billion years)-1
================
But in most of the quantitative cosmology stuff we do around this forum we don't use parsecs and Megaparsecs very much, and recession speed are rarely expressed in km/s. So both those units are rather foreign to the discussion.
The problem, then, is to get the all-important Hubble parameter into some handier form for our purposes.
All things considered, I think the most user-friendly, in particular beginner-friendly, is the conventional Hubble radius. At any given stage in history, the Hubble radius is the distance that is expanding at speed c. So, because of the basic v = H D law, in whatever units you work in it is always true that c = H R and so the Hubble radius R = c/H.
Therefore, if somebody tells you that the Hubble parameter is, say, 67.8 km/s per Mpc,
all you have to do is paste this verbatim into google:
c/(67.8 km/s per Mpc)
and you will get out a certain distance. But it will be in meters! So to force google to tell you the Hubble radius in light years you simply add the words "in light years" to what you paste in:
c/(67.8 km/s per Mpc) in light years
Then google will give you 14.4 billion lightyears.
=======================
That is easy to interpret as a percentage distance growth rate namely 1/144 percent per million years. You can always do that with the Hubble radius if you want to explain it to someone as a percentage growth rate.
And it also means that a sample distance of 1 Gly is growing at a speed of 1/14.4 c, that is slightly less than 1/14 of the speed of light. All the other growth speeds are proportional, so that is also a good way to picture it.
In the standard LCDM model, at any given time, all the cosmological distances (i.e. between pairs of CMB stationary observers) are growing at the same percentage rate, and what seems to be the most user-friendly way to package that information is in the form of the Hubble radius.
=======================
If you look at one of Jorrie's tables you can see what the Hubble radius has been in the past and what it is projected to be in the future. It has been increasing throughout history and is slated to continue increasing (but more and more gradually). So as it increases from the present 14.4 billion LY to, say, a future 17.3 billion LY, you can see that the percentage rate will decline from 1/144 to 1/173 percent per million years. You can always read off the percent rate from the Hubble radius.