How is dark matter thought to have formed a network scaffolding?

[Orodruin]

Do not confuse expansion rate with distance growth. In a universe with constant expansion rate, the distance between two comoving objects grows exponentially.

 

[hkyriazi]

Do not confuse expansion rate with distance growth. In a universe with constant expansion rate, the distance between two comoving objects grows exponentially.

I do get that if one defines the expansion rate as a percentage of current distance--calculated yearly or over some other time interval, I presume--the distance compounds like interest, and a constant expansion rate yields an exponential growth in size.

Am I correct in thinking there's a discrepancy between the above-posted figure (and its illustrated switch, about 7 billion years ago, from "Slowing expansion" to "Accelerating expansion"), and this statement (#32) by Kimbyd: "The actual rate of expansion (velocity/distance) is and always has been dropping"?

 

[Bandersnatch]

Am I correct in thinking there's a discrepancy between the above-posted figure (and its illustrated switch, about 7 billion years ago, from "Slowing expansion" to "Accelerating expansion"), and this statement (#32) by Kimbyd: "The actual rate of expansion (velocity/distance) is and always has been dropping"?

No, there's no discrepancy.
The curve of the bell is a velocity curve, since it relates distance traveled in time. The direction of its curvature shows the direction of acceleration (i.e. slowing expansion vs accelerating expansion).
The rate of expansion tells you - just as you described in the other paragraph above - by what fraction does the distance grow in unit time.
There's nothing contradictory in having the fractional growth go down over time and the velocity starting to accelerate.
I think you'll need to describe in more detail why you think there is one, before we can address it.

 

[hkyriazi]

No, there's no discrepancy.
[...]
There's nothing contradictory in having the fractional growth go down over time and the velocity starting to accelerate.
I think you'll need to describe in more detail why you think there is one, before we can address it.

OK, I'll give it a shot, though in reading over what I've written below, I'm not sure my fog has been lifted. ;-)

Am I correct in assuming that the folks who did the Type IA supernova data acquisition and analysis that has been interpreted as an accelerating expansion, and led to the hypothesizing of dark energy, thought they'd find instead that the amount of expansion per unit time has continually been decreasing (as in the lower half of that bell curve), and would eventually slow almost to zero, such that that bell curve would eventually have its two sides going essentially straight up (though not quite)? (And, would that constitute a "flat universe"?) I'm guessing that that initial, slowing expansion was thought to be due to the effect of gravity.

Also, am I correct in thinking that for the lower half of that bell curve to be accurate--i.e., the "size of the universe" was slowing its rate of increase--the rate of expansion (defined as a percentage of distance between "comoving objects" per time unit) had to be constantly decreasing, and by an amount larger than that required to counter the "compounding interest" aspect of that rate?

Finally, would it be correct to modify Kimbyd's statement from this: "The actual rate of expansion (velocity/distance) is and always has been dropping", to this: "The actual rate of expansion (velocity/distance) is and always has been dropping, but around 7 billion years ago the effect of gravity to slow the rate of expansion greatly dwindled, decreasing the decline in the rate of expansion to the point where the "compounding interest" aspect of the expansion rate took over, resulting in an increase in the growth of the universe's size per year"?

 

[Bandersnatch]

Yes, all of that looks fine.
Maybe apart from this bit:

but around 7 billion years ago the effect of gravity to slow the rate of expansion greatly dwindled

Insofar as there was nothing sudden or 'great' about it. The opposing effects of decelerating matter (and radiation) vs accelerating dark energy have been going on from the very beginning. At some point matter simply diluted enough for the (constant) accelerating effect to become dominant.

 

[Justin Hunt]

is 15 billion years really enough time for matter that was almost uniform to have formed into the structures of today? There is a lot of empty space between galaxies today and this movement initially would have been very slow at the start when the density was close to uniform. Would part of the solution be that the universe was much denser back then?

Also, was matter considered all bound at the start of the big bang? did parts of the big bang cause globs of matter to become unbound? Is there any discussion about when parts of the universe in general may have changed from bound to unbound or vice versa?