B Threshold of gravitational pull over dark energy

[rede96]

M⊙M⊙M_\odot is one solar mass. mmm and MMM are the two masses of the objects in the system.

Ah ok, got it. Thanks again.

 

[rede96]

You seem to want to have some simple rule you can use to classify objects in the universe. There isn't one.

Only for the purposes of understanding some basic underlying principles. If it helps to me to understand, nothing wrong with that. For example I was treating a system and all parts of that system as just a single mass, so to speak, so I could work out in today's DE dominated universe just where the threshold distance was that another system would no longer become gravitationally bound.

No, it's because the density of matter and radiation is now small enough that the cosmological constant becomes the primary factor that determines the dynamics of the universe's expansion.

And what is density... Mass per unit volume. And as distances increase volume goes up the mass/radiation density goes down. It's the same thing. But the point was that it is inertia from the big bang that caused expansion not dark energy as you've said. And my personal way of thinking about it is that only when the distances between comoving objects became great enough could dark energy take over and cause accelerated expansion. So very crudely the critical size of the universe was just over 2/3 of what it is now. (As I thought I read DE started to dominate about 4 billion years ago)

You really, really need to be careful about the distinction between moving apart and accelerating apart.

I'm not sure what context you mean this in? If something is accelerating apart it is moving apart. If the rate of change isn't important to the context, moving apart is fine. Or did I miss something?

In any case I found this thread really useful and helped to straighten a few things I hadn't understood properly. So just wanted to say thanks to everyone for their help.

 

[PeterDonis]

If it helps to me to understand, nothing wrong with that.

But I'm not sure it's helping you to understand, since you keep making incorrect statements.

And what is density... Mass per unit volume. And as distances increase volume goes up the mass/radiation density goes down. It's the same thing.

No, it isn't, because this naive intuitive reasoning doesn't explain why dark energy density doesn't also decrease as "distances increase". Nor does it explain why the density of matter (more precisely, non-relativistic matter) goes like the inverse cube of the scale factor, while the density of radiation (more precisely, relativistic matter and radiation) goes like the inverse fourth power of the scale factor.

In other words, "distances increase" is not the fundamental thing that is going on here. The fundamental thing is that the densities of dark energy, matter, and radiation are behaving differently along comoving worldlines.

the point was that it is inertia from the big bang that caused expansion not dark energy as you've said

Inertia from the big bang is why comoving objects are moving apart, yes. But it's not why they are accelerating apart. The latter requires dark energy.

my personal way of thinking about it is that only when the distances between comoving objects became great enough could dark energy take over and cause accelerated expansion. So very crudely the critical size of the universe was just over 2/3 of what it is now.

But this number, 2/3 of the current scale factor, if you try to derive it as we have been doing in this thread, should not be a universal number; it should depend on the masses of the comoving objects, since the distance at which two objects are just on the threshold of not being gravitationally bound depends on their masses.

If we calculate the critical scale factor on the basis of average densities, however, it is a universal number: heuristically, it's the scale factor at which the average matter density just equals the average dark energy density (radiation density can be neglected here because by a few billion years ago it was already much smaller than the matter density, because radiation density decreases faster).

If the rate of change isn't important to the contex

But it is important, which is why the distinction between "moving apart" and "accelerating apart" is important. Failing to recognize this has already tripped you up a couple of times in this thread; that's why I emphasized it.

 

[rede96]

Inertia from the big bang is why comoving objects are moving apart, yes. But it's not why they are accelerating apart. The latter requires dark energy.

Yes I know, where did I imply this wasn't the case?

No, it isn't, because this naive intuitive reasoning doesn't explain why dark energy density doesn't also decrease as "distances increase". Nor does it explain why the density of matter (more precisely, non-relativistic matter) goes like the inverse cube of the scale factor, while the density of radiation (more precisely, relativistic matter and radiation) goes like the inverse fourth power of the scale factor.

Actually it does, at least for two of them. I'll have to go back to my notes on FRW to understand why relativistic matter and radiation goes like the inverse fourth power of the scale factor as I can't remember.

But the reason non-relativistic matter goes like the inverse cube of the scale factor as distances increase is the same principle as a cube expanding with a finite amount of matter in it. That's simple and how we model expansion anyway. All I am saying is what is caused that 'cube' to expand initially was inertia from the big bang. And eventually the matter / radiation density reached a critical point, which will correspond to a specific scale factor / distance, and dark energy took over and accelerating expansion started.

As for dark energy how I understand it is it doesn't expand as its part of the structure of space / spacetime and is a kind of geometry not necessarily a density per se. Although modeling it on a constant energy density does work in the FRW equations.

But how I've come to think about it is like having a huge ball somewhere on the surface of the Earth and I put two small toy cars at the top of the ball and give them a push apart so they are traveling apart in opposite directions. They move apart slowly at first as there is some friction and the gradient isn't very big over small distances, but as I have given them a sufficient push, they continue to move apart until a point where the gradient increases sufficiently, gravity takes over and they start to accelerate apart. That's sort of how I imagine dark energy to work. As distances increase, the attractive force of gravity reduces sufficiently to allow expansion to accelerate.

Now I know my dark energy analogy isn't technically correct and there is a lot more for me to understand. But as a basic principle to explain things to a layman like me I don't see anything wrong with it.

 

[PeterDonis]

the reason non-relativistic matter goes like the inverse cube of the scale factor as distances increase is the same principle as a cube expanding with a finite amount of matter in it.

In a universe that is spatially flat, yes, this intuitive reasoning gives you the right answer. But it does not explain why the matter density still goes like the inverse cube of the scale factor in a universe that is spatially closed or spatially open, i.e., not spatially flat (which means the geometry of a spacelike 3-surface of constant time is not Euclidean).

I know my dark energy analogy isn't technically correct and there is a lot more for me to understand. But as a basic principle to explain things to a layman like me I don't see anything wrong with it.

The question is whether it leads you to make correct predictions.

 

[rede96]

In a universe that is spatially flat, yes,

Yes, of course. All of my thought process is based on the assumption of a specially flat universe.

The question is whether it leads you to make correct predictions.

That's why I am trying to get more into the Math as conceptually my understanding is stuck I think. It's just finding the time as I will have to go back to basics.

Anyway, thanks again for your time and patients.

 

[PeterDonis]

All of my thought process is based on the assumption of a specially flat universe.

Ok, fair enough. Since our best current model of our actual universe is that it's spatially flat, this is not an unreasonable approach. As long as you're aware that you won't necessarily be developing an understanding of the most general underlying laws, but only of one particular solution to those laws (the one that describes our actual universe).