Must (Ve) expansion of the universe be C?

[bobie]

It is valid for all objects 10 Mly away (neglecting local motion, those objects all have the same apparent recession speed). But not for objects 20Mly away. Or for the same object 1 billion years ago.

I am glad you say that, mfb, because that is exacly what I meant from the beginning and in post #37:

- they say that it has fluctuated and now indeed it is accelerating. That implies that you are aware of different rates at different times. Make an average and tell me what it is.

You take the averages of different epochs, make an overall average and there you have what seemed oscure in post #2: V_e, the average expansion rate of U

Yes, this is rough coincidence today, it has no special meaning (again, see previous posts). It was wrong in the past and it will be wrong in the future.
≈ instead of = is a big difference.

I hope you had read my reply to matterwave.
I am not referring to present or past value of 1/H₀, I am asking about the mere presence of H₀ in the formula, why in determining the age of U you need to refer/consider/ relate to the expansion rate.
If you do, there must be a relation, a reason I am sure, why? I am not aware of the necessity of such a relation as I showed in the balloon example

 

[mfb]

You take the averages of different epochs, make an overall average and there you have what seemed oscure in post #2: V_e, the average expansion rate of U

Then you get "current proper distance"/"age of the universe". What's the relevance of that value?

I am not referring to present or past value of 1/H₀, I am asking about the mere presence of H₀ in the formula, why in determining the age of U you need to refer/consider/ relate to the expansion rate.

Because there is no other way? You start with the current universe and work backwards until the distances become zero.

If you do, there must be a relation, a reason I am sure, why? I am not aware of the necessity of such a relation as I showed in the balloon example

Expansion rates are not arbitrary, they follow the FLRW equations (according to our measurements).

 

[marcus]

...
Expansion rates are not arbitrary, they follow the FLRW equations (according to our measurements).

That's the crux! If a member will not be satisfied with others' verbal interpretation of the Friedman equation (aka FLRW for Friedman Lemaître Robinson Walker) then if they are sincerely interested in learning they must be shown the equation and make an effort to assimilate it. At least I see no other way.

I made a graphic plot of T and 1/H, to illustrate the relation between them.
There is a thumbnail of the graph, and a little bit of explanation of the Friedman equation here:
https://www.physicsforums.com/showthread.php?p=4779726#post4779726
Click on the thumbnail there to enlarge. I'll try to also put the plot in line here:

The curves cross at around year 15 billion, that is a little over one billion years from now, in the future. It is not true that, at present, T = 1/H

To essentially repeat what several others have said: the present value H₀ is a key datum derived from observations and provides an important INPUT to the equation by which one figures out the estimated age T₀. The Friedman equation is what mediates between the two and that relationship is what has to be understood. There is no simple naive EQUALITY like T = 1/H

The Hubble radius (in Gly) is numerically the same as the Hubble time (i.e. 1/H) expressed in Gy. So the red curve gives the Hubble time in Gy as well as the Hubble radius. Either quantity is a reciprocal indicator of expansion RATE, not a measure of SIZE. You can see from the plot that the expansion rate is due to level off while distances continue to grow. The rate is due to level off at around 1/170 % per million years,i.e. the Hubble time 1/H is due to level off around 17 billion years, as the graphic plot indicates.

 

[PeterDonis]

But what we DO have are a large number of ways to determine the distance to an object, irrespective of the FLRW metric.

Not only that, we also have observed *relationships* between the different distance measures; and those relationships can be used to place significant constraints on the possible models that can explain the data. For example, see Ned Wright's cosmology tutorial here:

http://www.astro.ucla.edu/~wright/cosmo_02.htm

 

[julcab12]

For the sake of reference. Here is an animated chart in line with FLRW on curvatures.

http://background.uchicago.edu/~whu/intermediate/clcurvature.html"The animation shows two scenarios: for the yellow curve, ΩΛ is fixed to zero and ΩM gradually decreases, so that ΩK increases and the curvature is increasingly negative. And indeed, the peaks move to the right. For the blue curve, ΩK is fixed to zero (a flat universe) and ΩM gradually decreases (so that ΩΛ increases accordingly). This time, it follows that the peaks move slightly to the left as the amount of dark energy increases."

 

[marcus]

I've been trying to understand how a newcomer could, as may have happened in this case, get confused about the connection between the age of expansion (call it T) and the Hubble time (call it 1/H) or equivalently the distance version of the Hubble time (call it R = c/H). Since we've turned a page I'll bring forward a graph that may help:

...I made a graphic plot of T and 1/H, to illustrate the relation between them.
There is a thumbnail of the graph, and a little bit of explanation of the Friedman equation here:
https://www.physicsforums.com/showthread.php?p=4779726#post4779726
...

The curves cross at around year 15 billion, that is a little over one billion years from now, in the future. It is not true that, at present, T = 1/H...

To repeat for clarity, the Hubble time is just the reciprocal of the growth rate. The Hubble radius R is just equal to the Hubble time multiplied by c. If the time is 14.4 Gy, then the radius is 14.4 Gly (if one is a number of years the other is the same number of lightyears).

Since they are reciprocals, if the Hubble rate increases the Hubble radius must decrease, and viceversa. The Hubble radius R does not grow at the speed of light. If fact you can see that it is beginning to level out around 17 billion lightyears.

I think this is where an intelligent Noobie could get confused. When someone tells you the definition of the Hubble radius, if you don't listen very carefully you can easily get the wrong idea and think that it represents the "size" of the universe in some sense and that it is growing at the speed of light!

The Hubble radius is certainly not in ANY sense the radius of the universe! It is simply a way of keeping track of the rate that actual physical distances between pairs of stationary objects/markers/observers etc are increasing. The Hubble radius does not even have to grow--it can DECREASE while the universe is undergoing expansion, or it can increase but at an entirely independent rate.

The Hubble radius AT ANY GIVEN MOMENT is basically just the SIZE of those physical distances which are increasing to the tune of c, the speed of light, AT THAT MOMENT. It tells you what other distances (between CMB stationary markers as always) are doing, at that moment, because their speed of growth is always in proportion to their size. So Hubble radius embodies the same info as Hubble time 1/H or as Hubble rate H itself.

 

[marcus]

So here's a perfectly reasonable confusion that could happen to someone. they hear the definition:
"The Hubble radius is the SIZE of those actual distances (between stationary markers) which are growing by c at that moment."

And they say to themselves Ahah! I hear the word radius therefore we must be talking about the radius of the universe!

And they say Ahah! it sounds like the Hubble radius must itself be growing at the speed of light!

Therefore the universe has a definite known radius and a definite speed of expansion which is the speed that radius is growing!

Alas it is not so. The universe does not have a definite known radius and a well-defined "speed of expansion". That phrase is meaningless as far as we know. According to the standard model it has a percentage RATE of distance growth, not a speed.

And Hubble radius is not defined as a distance between a designated pair of objects each at CMB rest. It is defined as a critical size or threshold size, valid at a particular moment, dividing the distances growing < c from those growing > c.
that critical distance seems to change over time according to the Friedman equation---which is a model that fits massive amounts of data amazingly well and arises from the GR equation (currently accepted law of gravity and geometry). We can be pretty sure we understand (to good approximation) how H changes with time which amounts to the same thing as knowing how R changes, since it is the reciprocal c/H. In any case it should be clear that the Hubble radius is not itself subject to Hubble law distance expansion. It is not growing at the speed c! Indeed it is showing signs of leveling off and eventually changing very little if at all