# Is the Hubble constant, constant?

It seems to me that in an expanding universe where the expansion rate is accelerating, that the hubble constant will be greater for near stars than the constant for far stars that were receding at lower rate at the time the light from them was emitted.

So when I see a cosmology calculator that asks me to enter a Hubble constant and the values for Omega(mass) and Omega(lambda) do I enter the Hubble constant for near or far far stars and when new values for the Hubble constant are announced do they mean the Hubble far, near or average constant?

Garth
Gold Member
The Hubble Constant is not generally constant, it should really be called the Hubble Parameter.

The current figure of ~ 73 km/sec/Mpsc that is quoted is $H_0$ i.e. the value of H in the present epoch.

In one model, the old Hoyle/Gold/Bondi Steady State Theory, H would be constant over all time, an example of the now discredited Perfect Cosmological Principle.

Garth

marcus
Gold Member
Dearly Missed
So when I see a cosmology calculator that asks me to enter a Hubble constant and the values for Omega(mass) and Omega(lambda) do I enter the Hubble constant for near or far far stars and when new values for the Hubble constant are announced do they mean the Hubble far, near or average constant?
You enter the TODAY value of the Hubble parameter, like Garth says 73, or like 71 which was a common estimate 2 or 3 years ago and I'm in the habit of using.

Thanks :)

I was wondering why various sources seem to give various values for the Hubble parameter varing from mid sixties to mid seventies.

George Jones
Staff Emeritus
Gold Member
Let me expand a bit on what Garth said

The Hubble constant is constant in space, not constant in time. At any instant in time, let L be the proper distance from us to any galaxy. Then, at any instant in cosmology time t, v/ L is constant for *all* galaxies, independent of their proper distance from us. At some other instant in time t', v/L is still constant, but is, in general, not equal to the constant at time t, i.e., the value of this (spatial) constant changes with time. This constant is the Hubble constant.

Also, the acceleration of the universe and rate of change of the Hubble constant are somewhat independent. For example, at the present time, the value of the Hubble constant is decreasing with respect to time, even though the expansion of the universe is accelerating with respect to time.

Usually, cosmological calculators need H_0, the Hubble constant at t = now.

...
Also, the acceleration of the universe and rate of change of the Hubble constant are somewhat independent. For example, at the present time, the value of the Hubble constant is decreasing with respect to time, even though the expansion of the universe is accelerating with respect to time.
Now you have confused me again just when I though the fog was clearing :tongue:

Could you elaborate a bit more on that last statement? How does the current Hubble parameter get lower despite an accelerating expansion rate at the current time? I am sure you know what you are talking about, but I can not picture it at the moment

marcus
Gold Member
Dearly Missed
in standard LambdaCDM cosmology, which is what all the online calculators (AFAIK) implement and are based on, there is only one value of the Hubble parameter for the whole universe at the present moment

there is uncertainty about the right value to use, maybe 71 or maybe like Garth says 73, there is some plusminus errorbar

in the model, the Hubble parameter changes, but very slowly at this time, it is gradually declining towards around 55 or 60, to some asymptotic value, theoretically. but that change is much too slow to observe!

the Hubble parameter is defined in terms of COMOVING distance, that is, the actual real distance now today, if you could measure it with a prearranged string of assistants each at rest relative to the CMB (the microwave background) which means they are NOT at rest relative to the earth or the target object.

the Hubble parameter is the ratio TODAY of the recession speed at this moment, divided by the actual (comoving) distance at this moment
so the units of the parameter are speed (km/s) divided by distance (megaparsecs)
or any other choice of units of speed-over-distance. It boils down to reciprocal-time but conventionally one says km/s per Mpc.

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In the past the H used to be much larger, like 1000 or 10,000 in the early days, and you can actually SEE this if you use Morgan's calculator, because that calculator tells you, among other things, what the H was at the moment when the light which we are now receiving was emitted by the object, and began its journey to us.

To get Morgan calculator to work, you have to type in the current value for H (like 71) and the redshift of the object you are observing, and then it tells you things like the distance then when the light was emitted, and the distance now, when the light is received, and the recession speed then, and the recession speed now, and the Hubble parameter then.

Its helpful in getting an idea of how these quantities change.

You may well have been using the calculator (or Ned Wright's) and discovered all this already. But I will give a link in case somebody else wants it.

http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

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in standard LambdaCDM cosmology, which is what all the online calculators (AFAIK) implement and are based on, there is only one value of the Hubble parameter for the whole universe at the present moment

there is uncertainty about the right value to use, maybe 71 or maybe like Garth says 73, there is some plusminus errorbar

in the model, the Hubble parameter changes, but very slowly at this time, it is gradually declining towards around 55 or 60, to some asymptotic value, theoretically. but that change is much too slow to observe!

the Hubble parameter is defined in terms of COMOVING distance, that is, the actual real distance now today, if you could measure it with a prearranged string of assistants each at rest relative to the CMB (the microwave background) which means they are NOT at rest relative to the earth or the target object.
Thanks marcus,

that sort of helps.... but... if one of the assistants is right next to the target and rest with the CMB (locally) and if the target is at rest with the CMB (locally, which on average it will be) then the assistant must be at rest with the target. ?

George Jones
Staff Emeritus
Gold Member
Now you have confused me again just when I though the fog was clearing :tongue:

Could you elaborate a bit more on that last statement? How does the current Hubble parameter get lower despite an accelerating expansion rate at the current time? I am sure you know what you are talking about, but I can not picture it at the moment
Here in Saint John we do https://www.physicsforums.com/showthread.php?p=1603925#post1603925".

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marcus
Gold Member
Dearly Missed
Thanks marcus,

that sort of helps.... but... if one of the assistants is right next to the target and rest with the CMB (locally) and if the target is at rest with the CMB (locally, which on average it will be) then the assistant must be at rest with the target. ?
Right!

marcus
Gold Member
Dearly Missed
kev,
it isnt customary but I have to pay a flat out compliment here,
you SHOULD notice an apparent contradiction between the idea that the expansion is accelerating and the fact that H is decreasing (tapering down to something around 55-60 as I recall). it shows thinking to notice that seeming contradiction

George Jones probably covered this in his reply, but I will add a comment.

You know that the cosmology model uses the FRW metric and that a(t) is the spatial scalefactor in the formula for that metric. a(t) is sometimes called the size of the universe or the average distance between galaxies, to give it some intuitive feel. But concretizing can be a bother. Suppose the universe is spatial infinite so it has no welldefined size. Better to think of a(t) as an abstract scalefactor in the distance formula. Usually normalized so that a(present) = 1

well what accelerating expansion means is simply that a'(t) is increasing
or that a"(t) is positive. I am writing time-derivative with a prime.

On the other hand what is H(t)? If you think about it you see that H = a'/a

that is the universal ratio (at this moment) of recession-speed to distance.

Loosely speaking, a' is the speed at which something at distance a is receding, if you put in units so it makes sense. So you can actually even DEFINE H(t) as the ratio a'(t)/a(t).

Now you can see that H(t) could very well be decreasing, even though the numerator was increasing, just as long as the denominator was increasing enough faster to outweigh it. And that is what is happening. The scalefactor a(t) is increasing percentagewise faster than its timederivative a'(t). The acceleration is really very slight. So the ratio a'/a is actually declining.

this is all what the model says, the changes are too slow for us to detect so it is not something you measure. but if you assume the model, which most do because it fits the data nicely, then that's what's happening. only an apparent contradiction

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So in other words, are you guys saying that the Hubble constant from a range of here to 3 million light years is slowing down towards 60 km/sec per Mpsc but towards the outer edges of our expanding universe it is actually accelerating?

marcus
Gold Member
Dearly Missed
So in other words, are you guys saying that the Hubble constant from a range of here to 3 million light years is slowing down towards 60 km/sec per Mpsc but towards the outer edges of our expanding universe it is actually accelerating?
I can only speak for myself. No that is not what I am saying.
Cosmology is not a verbal science. It is a mathematical science. So if you try to think in words you will often get confused.
What they mean by "universe is expanding" is that a'(t) is positive

What they mean by "expansion is accelerating" is that a''(t) is positive. Or putting it another way, that a'(t) is increasing.

the HUBBLE parameter is totally something else. It is the RATIO of a'(t) and a(t). So it can easily be DEcreasing even though the universe is expanding and the expansion is accelerating.
================

The math is simple and could easily be taught in highschool. Anywhere where you learn about the slope of a function of time. The time-derivative. In fact as it happens the scalefactor a(t) is a really simple-looking curve. I used to have a link to a picture of it.

But people get messed up when they try to discuss this business in words, because words like "expansion of the universe is accelerating" are automatically very vague. Don't mean anything definite until you write down what they say mathematically.
=================

Anyway, at any given moment of universal time (defined by the CMB restframe) the Hubble parameter is the same throughout the universe. And the universe has no edges. So it couldnt be different at the edges----for two reasons.

It couldnt be different at the edges because it is the same throughout all space. It couldnt be different at the edges because there are no edges (in the standard cosmology model)

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This is what I have heard about the Hubble Constant. Hubble had discovered that light moving away from the stars of distant galaxies was "red-shifted", not "blue-shifted" and as a result, these stars were moving away from us here in our solar system.

Hubble found that some galaxies were moving slowly away from us while some were racing away from us tremendously faster (with the exception of the very few galaxies that are close to us which actually appear to be moving towards us).

Hubble found that the closer galaxies moving outward from us were moving at slow velocities but the galaxies farther away from us were speeding away from us at tremendous velocities. Hubble's constant tells us that recessional velocity not only increases with distance but also is directly proportional to distance.

So far am I correct?

Question -Is the universe expanding at an accelerating rate all around us in every direction, or just in one particular direction?

What is causing this expansion, is it the dark matter that holds everything in place or could it be vacuum energy (dark energy)?

marcus
Gold Member
Dearly Missed
This goes for everybody.
Be sure you have read the introductory tutorial on expansion cosmology published in the March 2005 Scientific American "Misconceptions about the Big Bang" by Charles Lineweaver

Standard model cosmology is not matter expanding into empty space (that would have a kind of edge, the outer edge of the expanding matter, so that's wrong)

There is a princeton.edu link to an online copy the Lineweaver SciAm article. It has been recommended many many times by many different people. I'll hunt it up. Here it is as a PDF file. It is worth downloading and keeping handy. Valuable entry-level resource.

Despite what I said, Lineweaver uses words and pictures and does a really good job on the basics. He manages OK without using mathematics expressions. The exception rather than the rule.

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Does "dark matter" hold the stars in its place in galaxies as they rotate around their black hole centers? Also I heard that the total mass of all the galaxies can only be accounted for 30% by the matter we can see, the rest is made up of "dark matter". Is this all proven or still speculation?

marcus
Gold Member
Dearly Missed
Hubble's constant tells us that recessional velocity not only increases with distance but also is directly proportional to distance.

So far am I correct?
Correct. At a particular moment, the present recession speed is proportional to the present distance, and the proportion is the same throughout all space (at that moment)

Question -Is the universe expanding at an accelerating rate all around us in every direction, or just in one particular direction?

What is causing this expansion, is it the dark matter that holds everything in place or could it be vacuum energy (dark energy)?
Same in all direction, and from everybody's perspective. No preferred direction. No preferred standpoint.

The standard model does not say what started the expansion. (Some quantum gravity models have it start with a bounce---gravity repellent at very high density. The classical model has no explanation.) Einstein equations say that once expansion starts it will CONTINUE unless attractive force of matter is sufficient to halt it and turn it around. By present measurement the density of matter is not enough to do that. Expansion does not need a cause in the present environment. Once begun it continues.

Dark energy has a slight accelerating effect, but we would still be having expansion even if there were no dark energy. If you believe the Einstein equation (which is our most successful theory of gravity so far) we don't need any further explanation for why expansion, once started, is continuing.

Be sure you have read the introductory tutorial on expansion cosmology published in the March 2005 Scientific American "Misconceptions about the Big Bang" by Charles Lineweaver

.

It is the rare introductory article which is non-mathematical but makes the basics of cosmology really clear.

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Thanks for the link. I appreciate it and I will read it.

PS - I wish Einstein was alive to hear all this information discovered by Hubble and the rest of our scientists today. I think he may be able to link the expansion to something or come up with why it is happening and/or how it originated.

Something tells me if we all see rapid expansion at the same velocity for different distances anywhere we are in the universe this might have something to do with relativity.