A layman's guide to the accelerating expansion of space

[marcus]

Egregious, Bander's suggestion is good. distance expansion is not like ordinary motion, nobody gets anywhere by it, everybody just becomes farther apart. no goal is approached by anybody, relative positions (e.g. longitude and latitude on the balloon if you like that metaphor) do not change. So the general pattern of geometry change---of distance expansion---is not like motion thru space we are used to, and not subject to same rules.

Distance expansion is not limited by the speed limit we have for local motion thru space. nobody is zooming past anybody or outracing a photon of light. But the distances to most galaxies we can see with telescope are increasing faster than light. (so if they sent us a message TODAY it might never get here, but that doesn't matter because they already sent us years and years worth of light which is on its way and will be arriving for billions of years to come so we can observe them they are part of our universe and we are part of theirs.)

 

[PeterDonis]

if we could look further to the time of the Big Bang (which we can not cause the universe becomes opaque to light at a certain point), those two regions would actually be at the same location

No, they wouldn't, because the "Big Bang" singularity is not part of spacetime, and our current models do not even include it as a limit. Instead, there are various speculations about how inflation got started, none of which involve explosive expansion from a single point.

In the idealized FRW spacetimes, there is an initial singularity, but it is still not actually part of the spacetime; it's only present as a limit. But even in these models, two distinct "comoving" worldlines emerging from the initial singularity are causally disconnected until some finite amount of cosmological time has elapsed--how much time must elapse depends on how "separate" the two worldlines are (how much their spatial coordinates differ in the standard FRW coordinate chart). To really see how this works, you need to look at a conformal diagram, which makes causal relationships clearest; Ned Wright's cosmology tutorial contains a good one (see the "Horizon Problem" section at the bottom of the page).

(In fact, the term "Big Bang" should not even be used to refer to the initial singularity; it is properly used to refer to the hot, dense, rapidly expanding state that existed at the end of inflation.)

at one time they were very close together, in the same general location, effectively contiguous

"In the same general location" does not guarantee "causally connected", which is the relevant concept. See above.

 

[Berenices]

Okay can I clean up one topic.
Say you had two distant galaxies just the right distance away from each other that the effects of gravitational acceleration and dark energy were essentially the same.
I am fairly certain that dark energy does not effect the actual velocity of objects but only the distance from each other that two coordinates are observed to be over time. As gravity has an exponential acceleration over time, would the two galaxies eventually get to the point in which their speeds towards each-other overcome the stretching of the space in between them?

 

[valenumr]

I think it is an interesting thing to note, what Valenmur calls "constant expansion" is in some ways exponential.
After one period of time the distance from green to blue doubles. After another equal period, that distance doubles again.

The same can be said for the distance from green to purple, and for the distance from green to red.

Is that a standard description of what is meant by constant expansion?

I would probably represent that as dr/dt = k r.
dr/r = k dt
ln r = k t
r = e ^(kt)

r = r_0 * 2^t

That is what I meant by constant expansion in this context, and your interpretation is exactly correct. By constant in this example, I mean space is expanding at a constant rate for all time, i.e. one (arbitrary) unit of space becomes two after one (arbitrary) unit of time. Because the expansion is a continuous process, this looks like an exponential. At the same time, you should also see that the recession rates are linear with respect to distance. So in this case, the redshift / distance graph would be a perfectly straight line.

So good question, because it really highlights all the key points I wanted to get across.