Does mass slow the expansion of space?

[AndyFin]

I read that the mass of the universe slows the expansion of the universe. I also heard that if the mass of the universe was above a critical value the universe would contract. I believe this is called the big crunch scenario. And that it is currently not considered a probable scenario.

Is this true?

I have some follow up questions if this is really true.

The next question is what do we understand by space contraction in the big crunch scenario, Does this mean the mass then goes to the center of the universe but the piece of space I am currently sitting in is in the same place after the big crunch, or has the space also actually moved so that it is at the same point as the me? ( of course under the condition that a big crunch happens and I live that long and i don't move in space - Neither very likely I know, but anyway.

 

[Bandersnatch]

Hi AndyFin, welcome to PF.

Yes, it's true.

By space contraction we mean the same thing as by space expansion - nothing moves, but all distances change at the same rate. There is no unique centre of the universe. All observers, regardless of where they are, see themselves as being at the centre - they don't see themselves as moving, but all see the universe contract to/expand from where they are.

 

[AndyFin]

Hi Bandersnatch, thanks for the answer. I really appreciate it. However I am really struggling to understand this space doesn't move thing.

Are you saying that my space doesn't move , or that in general a volume of space that is some (large) distance away from doesn't move relative to me . ie its distance from me gets less and it gets closer to me, but it is not moving relative to me as the big crunch scenario unwinds?

I understand that I will not move locally, but I don't understand that " all distances change, but nothing moves". Can you help me to understand this. I would have (perhaps rather naively) thought that if the distance from me to a far away galaxy changes, and that locally in my reference frame neither I nor the space surrounding me is moving, and for some alien cousin in the far away galaxy neither he nor the space surrounding him is moving in his reference frame, But, as he is receding (Say I see a redshift in his skype signal hahaha so I know he is receding) then surely the space surrounding him is also moving away at the same rate ( at least relative to my reference frame) Can you please let me know what is wrong with my logic.

So as space doesn't move then at any big crunch, will the volume of the space be the same before the big crunch, as it is now now and as it was at the big bang? Would the volume of space in big crunch scenario be smaller

Or is a change of volume not a movement? In the big crunch scenario, does the volume of the universe decrease?

Or is the explanation that change of distance with time for space is not the same thing as change of distance with time for a mass like my old body for instance,? I hope you can see why I am a little confused here.

Is the problem here the terminology? Is the contraction (or expansion) from a mathematical point of view not the same as a contraction as defined as getting smaller and decreasing ?

 

[Bandersnatch]

what is wrong with my logic.

Nothing, essentially.

It's just that, like with many other 'obvious' concepts, like distance, speed, or age, motion in cosmology requires some extra care when using, so that we all know what we actually mean and not get confused.

I said nothing is moving for two reasons - as the space expands (or contracts), the relative positions of objects in the universe don't change (disregarding small local motions). You do get changing distances, but if something was at your 9 o'clock, it'll stay there throughout the history. Furthermore, this 'recession' (or the opposite) is a General Relativistic effect, where all objects carried away by the expanding/contracting space are in free fall, following straight lines in space-time (geodesics), and whether they approach or recede is due to how the energy content of the universe curves the geodesics (much like with regular gravity described by GR).

However, the distances between objects still change - so one could very well say, hey: that's motion! And in fact, there are many who do. You see, there is no universally accepted usage of the word here. Still, choosing not to call this 'recession' (in case of expansion) 'motion' allows you to do two things:
- avoid the inevitable confusion when you realize that recession can and does carry away objects at recession velocities in excess of the speed of light
- get used to using so called 'comoving coordinates', employed throughout modern cosmology to describe the evolution of the universe. In these coordinates, the change of distances is factored out, so everything always stays where it is (i.e., relative to each other, in those coordinates). The whole of expansion or contraction is then relegated to one function called 'scale factor', a(t), describing how to scale the distances at different times in history (e.g. now, everything is ~1090 times farther away than it was ~13.8 billion years ago).

So, if you think about contraction in the big crunch scenario, while using the comoving coordinates, you see that every observer stays where they are, but as time progresses the scale of distances between them gets shorter and shorter.
Yes, you could say that everything 'moves' closer together, but it's a special kind of motion, somewhat unlike what we're used to.

Or is it that change of distance with time for space is not the same thing as change of distance with time and space for a mass like my old body for instance,?

Right, when talking about the expansion/contraction of the universe, you are always only concerned with large-scale objects moving in relation to each other. These objects need to be sufficiently far away for local gravitational effects to lose dominance. I.e., the 'all distances change' doesn't actually include distances between molecules in your body, in the solar system, or even on the galactic scale. In other words, expansion/contraction doesn't affect local gravitationally bound systems. You need to look at superclusters to see the effects of expansion of space.

 

[phinds]

@AndyFin I recommend the link in my signature (and that you read it all the way through)

 

[AndyFin]

Ok super, I think I am starting to understand a bit better