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

[hkyriazi]

No, this is pretty far off. The Cosmological Constant isn't at all fundamental to spatial expansion, and it doesn't contribute any non-linearities. In fact, the CC part of the Einstein Field Equations is the one part that is fully linear.

Ah, right. I was confusing spatial expansion with the *acceleration* of spatial expansion attributed to dark energy. (Am I correct in thinking that the CC is directly related to that?)

 

[kimbyd]

Ah, right. I was confusing spatial expansion with the *acceleration* of spatial expansion attributed to dark energy. (Am I correct in thinking that the CC is directly related to that?)

Yes, that's correct.

Though the terminology around the accelerated expansion is confusing. The actual rate of expansion (velocity/distance) is and always has been dropping. The acceleration comes in because if the reduction in the rate of expansion is slow enough, then as objects move further away they'll recede at higher velocities.

That's what the cosmological constant does: it places a floor on the rate of expansion. In the far future, the rate of expansion will be a constant determined by the cosmological constant.

This floor on the rate of expansion does two main things:
1) It tends to make it a little bit harder for structures like galaxies and galaxy clusters to form, as the cosmological constant makes gravity repulsive at large distances. Large extent and low density make structures more vulnerable to disruption by the cosmological constant. This shapes what kinds of objects are more common in our universe.
2) At late times, by placing a floor on the rate of expansion, it causes an eternal, accelerated expansion where (eventually) objects are moving away from one another at an exponential rate.

At very early times, the cosmological constant was simply too small to have any impact at all, so it likely is utterly irrelevant when considering questions for the very early universe such as what caused the expansion in the first place.

 

[hkyriazi]

Yes, that's correct.

Though the terminology around the accelerated expansion is confusing. The actual rate of expansion (velocity/distance) is and always has been dropping. The acceleration comes in because if the reduction in the rate of expansion is slow enough, then as objects move further away they'll recede at higher velocities.

Thanks. This is news to me, and I'll give it some careful thought. It's reminiscent of when congress critters say they're decreasing spending, but actually are merely decreasing the rate of increase in spending.

 

[Bandersnatch]

I'll give it some careful thought.

It's educational to start off with some clearly unphysical models of expansion, that nonetheless provide a set of good intuitions by virtue of being simplified.
For example, consider a Milne model, which is one where the universe is expanding steadily - neither accelerating or decelerating.
This means that any given galaxy that you observe to have some recessional velocity at a given time, will retain this velocity forever (and has had it since the beginning).
But, the value of the Hubble parameter is still going down, because it tells you by what percentage of their current value do all distances grow per unit time. So, a galaxy starting off e.g. 1 billion light-years (Gly) away, and always receding at 1 Gly per 1 billion years (Gyr), will after 1 Gyr be 2 Gly away = distance measured between 0 and 1 Gyr has grown by 100%. After another billion years, it will be 3 Gly away = the distance measured between 1 and 2 Gyr has grown by 50% only, even though the galaxy keeps receding at a steady pace. After another Gyr it's 33% and so on.

If you treat the Milne model as an edge case, then it's perhaps easier to see that any model where galaxies experience deceleration of their recessional velocities will have the Hubble parameter go down even faster. Whereas if they experience acceleration, the Hubble parameter will either go down slower (if the acceleration is less than exponential), don't go down (if the acceleration is exponential) or go up (if the acceleration is faster than exponential).

 

[hkyriazi]

Kimbyd and Bandersnatch, it's difficult to reconcile a slowing expansion rate with this figure (attached), from the Hubblesite: http://hubblesite.org/image/1037/news_release/2001-09I

I do recall reading at various times that some value or other was close to zero, meaning that the expansion was slowing, but such as to asymptote, never truly stopping, but practically so (ensuring that there'll be no "Big Crunch," as gravity reverses the expansion). Those jibe with your comments, but someone may have to make this entry at Wikipedia more clear: https://en.wikipedia.org/wiki/Accelerating_expansion_of_the_universe

 

[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?