# Why space expansion is limited to scales larger than galaxy clusters?

1. Oct 25, 2013

### Andrea Panza

Hello everyone,
I have a question about metric expansion of space.
According to Wikipedia (ok probably is not the best source, but I have only a qualitative understanding of physics) the expansion occurs only at scales larger than galaxy clusters.
http://en.wikipedia.org/wiki/Metric_expansion_of_space
Wikipedia says that this is due to the fact that at smaller scales the gravity prevents this expansion.
What I don’t understand is why since gravity also works through space.
What I mean is that I understand that we will first lose contact with distant bodies but if the universe is expanding in an accelerated way two bodies that are one meter apart sooner or later (extreeeeemely later) will get more and more separated and will exert a lower gravitational pull on eachother.
For what I understand an ever accelerating space expansion should ultimately rip all the matter apart, since at a certain point even quarks will be pulled apart faster than the speed of light preventing gluon interactions (what I mean is that in every moment more space is created than the one in which the strong force is propagating).
I can see three possible explanation why this will not occur:
-On theory maybe the my assumption is correct, but the timescale for it to happen is so big that all the matter will decay first through other mechanism (like proton decay)
-My understanding of the acceleration of the expansion is wrong: the acceleration is not exponential-like, but is asymptotic to a limit.
-I’m just wrong and I should ask on PF.

Thanks a lot in advance

2. Oct 25, 2013

### marcus

These are reasonable questions to ask! especially because in the public media it is not clear what is meant by the words "distance" and "expansion" when we're talking cosmology. "Acceleration" can have different meanings. there are some conceptual preliminaries to get thru.

CMB rest: An observer is at rest with respect to the Background of ancient light if the CMB looks the same temperature in all directions. Motion relative to Background makes the observer see a doppler hotspot ahead of him. The solar system motion relative to CMB has been measured fairly precisely and is corrected for in observations.

Universe time: This is time as measured by observers at rest anywhere in the universe, as long as the observer is not so deep in some gravity well that his clock is slowed significantly by that. Think of observers at rest out in intergalactic space where the gravity effect is weak. This is the universe-wide standard time that cosmologists use in making cosmic models.

Proper distance: This is distance *at some definite moment of time* that you would measure if you could stop the expansion process long enough to measure it by some conventional means like timing a radar beep.

Percentage expansion rate: This is what the "Hubble rate" tells you. It gives the fractional expansion per unit of universe time. This rate is actually DECLINING according to standard cosmic model.
It is about distances between observers at CMB rest.
The distance between two stationary observers is currently increasing 1/144 % per million years and that rate has been declining throughout expansion history and is expected by cosmologists to continue to decline. The asymptote being approached is estimated to be 1/173% per million years.

This doesn't mean there can't be "ACCELERATION" in terms of a given separation's growth ("recession speed") if you pick two stationary observers and watch the size of their separation grow over time.

If you start a savings account at a bank and the bank uses a slowly declining percentage interest rate your savings can still grow at an accelerating DOLLAR rate because the principal is growing. There doesn't need to be any contradiction. As long as the bank reduces the percentage interest rate on savings accounts sufficiently SLOWLY, your account in dollar terms will grow almost exponentially, and so there will be accelerating growth in dollar terms.

Local structures sizes are not affected because they are held together by physical bonds. Crystalline bonds, metallic bonds, molecular, gravitational etc. The two ends of a strong metal yardstick that is say 100 million lightyears long cannot both be at CMB rest. If one end is at rest then the other end must be moving at the rate of 1/144 % of the speed of light relative to the CMB. That is simply required in order for the yardstick to stay the same length, which it must for physical reasons if the metallic bonds are strong enough.
Likewise galaxies, held together by gravitational bonds, can stabilize at some size and stay that size.

Last edited: Oct 25, 2013
3. Oct 28, 2013

### Andrea Panza

Hi Marcus,
as usual thank you for your answer, however I'm afraid I didn't get all the explanation.
I understand that since CMB is the most distant observable phenomenon we can use it as reference (and I understand that if we could observe something older than CMB, CMB itself would not be at rest with this other hypothetical phenomenon).
I also understand (thanks to your bank account example) that you can still have an almost exponential growth even with a declining rate of expansion, however I didn't understand if this is the case with our universe.

What I don't understand is why the bar remains intact and it is probably due to some severe misconception about space expansion, I'll try to explain what I think in the hope that you and the other people in the forum could correct me.
-We observe objects receding from each others and we know observing the distant past that the matter/energy density of the universe decreased, and, in order to obtain this, the volume of the universe must have increased.
-The universe is not a cloud of gas expanding in an empty box, in the case of the gas the molecules recede from each other and occupy empty volumes of space that already exist in the box. Since there is nothing outside the universe, there is no such empty volume outside, so the universe expands in itself creating more space.
-Usually the expansion of the universe is pictured using an analogy with dots on a balloon that gets inflated: if we draw dots on the balloon the distance between them increases over time the more we inflate the balloon, however we could realize that the distance is increasing because we measure it with a meter that is outside the balloon.
If we draw two points A and B on the balloon and we unite them with a segment (an arc of circumference) and divide this segment in 10 subsegments, when we inflate the balloon they will remain 10 segments.
We know that this is not happening in the universe expansion because WE NOTICE the expansion: if lights travels one unit per second it will still take 10 seconds to get from A to B, despite the fact that the unit expanded compared to its previous size, if this was the case we would not notice an increase in distance.
Since we see that the light is redshifted it means that its wavelength has increased so it means also that an oscillation happens in more units of space and not the same number of longer units.
To come back to the balloon analogy it is like a case in which we progressively divide the arc in an higher number of segments to keep their original length.
But if more space comes into existence two points that before were in contact could be eventually get separated and if those two points were occupied by atoms involved in a molecular bond that bond should break.
So I expect that if we consider one end of the bar at rest with the CMB we will see the other end of the bar moving, but at the same time I expect the bar to lose coherence and get fragmented in ever thinner slices (i.e. the bar density decreases over time along the length).

I hope you can clarify where I'm wrong.

Thank you all in advance