Why isn't the pull of gravity neutral on large scales?

[PeterDonis]

can the Friedmann equations be derived without using Newtonian gravity?

Of course. They are derived from the Einstein Field Equation. That's how they were originally derived, and that's the actual justification for them. The Newtonian derivation, as I said, is just heuristic.

if I imagine 3 shells A, B and C arbitrarily spaced in a isotropic and homogeneous universe so that no shell overlaps with another. As I understand it, observers at the center of A, B and C would see any matter within their shell being pulled towards them.

Observers at the center of A, B, and C would see any matter within the radius a, b, c of their shell being pulled towards them, yes. But, and this is the crucial point, that statement is true regardless of the radius of the shell. In other words, observer A could just as well pick a shell that was large enough to include observer B (or C or both), and then he would observe B (or C or both) being pulled towards him. Similarly for B and C.

from what I understand about how the universe is modeled, in a matter dominated universe (e.g. no dark energy) then any observer would see all matter moving in towards them. Which seems to contradicts what observes in the 3 shells would see.

No, it doesn't. See above. The only issue that arises, with the Newtonian derivation, is that allowing the shell to be arbitrarily large, while still maintaining a constant density of matter everywhere, is not really possible in Newtonian physics; Newtonian physics would require the matter density to go to zero at some finite shell radius (otherwise the gravitational potential energy would not be bounded).

 

[rede96]

http://www.physics.umn.edu/classes/...ds/399811-FriedmanEqDerivation.pdf?download=1

Thanks for that. I don't quite get the Math, but reading the conclusions helped.

But it doesn't. It's exactly the same statement. After all, the centres of any two spheres are accelerated towards the third

Ah of course, got that now thanks.

Of course. They are derived from the Einstein Field Equation. That's how they were originally derived, and that's the actual justification for them. The Newtonian derivation, as I said, is just heuristic.

Ok great. I'll see if I can find any cosmology lectures on that. Cheers.

Observers at the center of A, B, and C would see any matter within the radius a, b, c of their shell being pulled towards them, yes. But, and this is the crucial point, that statement is true regardless of the radius of the shell.

I get that now thanks, but being honest I still struggle with understanding the physics behind the how. I think this is where I confuse myself in my visualization.

I imagined the situation to be analogous to a long string of tennis balls, each connected to each other by lengths of elastic. If I move all the tennis balls away from each other equally, then obviously there will be a force created from the elastic between each tennis ball which wants to contract the system. If the ends were not bound and I let go all the tennis balls, then this could happen freely. However if I had an infinity long string of tennis balls then I thought for any smaller group of balls, as there was an infinite amount of force either side in both directions, then it would cancel out and be as if the ends were bound. Hence the system could not contract, even though the force remained.

However I am guessing that an infinite string of tennis balls as mentioned above would still collapse on itself? Or is the analogy just not applicable?

 

[PeterDonis]

I'll see if I can find any cosmology lectures on that.

See pg. 223 of Sean Carroll's lecture notes:

https://arxiv.org/pdf/gr-qc/9712019.pdf

 

[PeterDonis]

Or is the analogy just not applicable?

I would say not, because the actual GR model of what is going on does not assume a static background space, which your analogy does. Your analogy does, IMO, raise a similar issue with the Newtonian derivation to the one that I mentioned before--that you run into problems if you have an infinite expanse of matter.

 

[rede96]

See pg. 223 of Sean Carroll's lecture notes:

Ok, great. Thank you.