Curvature of spacetime by gravity and the flat universe?

[Dagl1]

Hello everyone,

Excuse me for my thorough lack of understanding of this topic but I was reading some of Einstein's notes on relativity & the shape of the universe and this made me thinking.
I have always "understood" the idea that gravity warps space time through the trampoline analogy. The problem in my thinking is that if gravity curves space time, shouldn't the entire universe be a ball/spherical? As it contains matter everywhere, which would warp it inwards to itself (or maybe it becomes a doughnut shape?). I know that from experiments we have verified the cosmological constant (?) to be 1 or as close to 1 as we can verify experimentally, thus meaning that the universe is "flat" when looking at it zoomed out enough. So if my understanding is correct of these two things, the question becomes; what makes it flat and not a doughnut shape?

Possible answers I have myself are;
1. I am misunderstanding the flatness of space and the curvature of spacetime caused by gravity (maybe they don't talk about the same type of "curvature/flatness")
2.  Dark energy acts as negative mass (I don't know if this is true, but I seem to remember such an explanation of Dark Energy).
3. We don't know.

If anyone could please enlighten me or point out the errors in my thinking, that would be great! My mathematical skills aren't that great, so if math is to be involved, could you explain it in some more simple conceptual style as well;p?

Thanks in advance,

Dagl

[beecee]

3 hours ago, Dagl1 said:

Hello everyone,

Excuse me for my thorough lack of understanding of this topic but I was reading some of Einstein's notes on relativity & the shape of the universe and this made me thinking.
I have always "understood" the idea that gravity warps space time through the trampoline analogy. The problem in my thinking is that if gravity curves space time, shouldn't the entire universe be a ball/spherical? As it contains matter everywhere, which would warp it inwards to itself (or maybe it becomes a doughnut shape?). I know that from experiments we have verified the cosmological constant (?) to be 1 or as close to 1 as we can verify experimentally, thus meaning that the universe is "flat" when looking at it zoomed out enough. So if my understanding is correct of these two things, the question becomes; what makes it flat and not a doughnut shape?

Possible answers I have myself are;
1. I am misunderstanding the flatness of space and the curvature of spacetime caused by gravity (maybe they don't talk about the same type of "curvature/flatness")
2.  Dark energy acts as negative mass (I don't know if this is true, but I seem to remember such an explanation of Dark Energy).
3. We don't know.

If anyone could please enlighten me or point out the errors in my thinking, that would be great! My mathematical skills aren't that great, so if math is to be involved, could you explain it in some more simple conceptual style as well;p?

Thanks in advance,

Dagl

Firstly the factor that determines whether the universe is flat, is an energy  density parameter we call Omega. That is as close to 1 as our precision allows which tells us that the universe/spacetime is flat....meaning that two parallel beams of light will remain parallel. That total mass energy density includes DM, DE and the baryonic matter we are familiar with.

Also the trampolin analogy is a 2D analogy attemting to explain spacetime warpage in 3D plus time. Hence the difficulty and dangers in taking analogies too far.

[Carrock]

From https://en.wikipedia.org/wiki/Zero-energy_universe

Quote

A gravitational field has negative energy. Matter has positive energy. The two values cancel out provided the universe is completely flat.

This is a quite old idea, and an oversimplified description - see beecee's response - but does indicate how the universe can be flat on a sufficiently large scale.

[Strange]

With an even distribution of matter, there would be no curvature (imagine the rubber sheet being pressed evenly, it would remain flat). 

So the presence of mass, by itself, doesn’t tell us about the overall curvature

[swansont]

6 hours ago, Dagl1 said:

Hello everyone,

Excuse me for my thorough lack of understanding of this topic but I was reading some of Einstein's notes on relativity & the shape of the universe and this made me thinking.
I have always "understood" the idea that gravity warps space time through the trampoline analogy. The problem in my thinking is that if gravity curves space time, shouldn't the entire universe be a ball/spherical?

The ball in the trampoline doesn’t give you a sphere.

[Carrock]

1 hour ago, Strange said:

With an even distribution of matter, there would be no curvature (imagine the rubber sheet being pressed evenly, it would remain flat). 

So the presence of mass, by itself, doesn’t tell us about the overall curvature

It would only necessarily be flat in three spatial dimensions.

If e.g. the density were greater than critical, the universe would eventually stop expanding and contract i.e. it would be a closed 3-sphere.

Parallel light beams would converge.

[Dagl1]

@everyone thank you very much and sorry for my late reply, was out and about this weekend.

I think I understand why I was confused (I did not consider the fact that equal distribution of mass would lead to a "trampoline where everything is equally pressured down" and for some reason I thought that with enough mass the other parts of the trampoline would form a ball.

Thanks!

[Mordred]

As Beecee mentioned the curvature term isn't directly related to a physical shape as per se, but is a descriptive of how the density terms affect the light paths (worldlines). A flat universe means the wordlines remain parallel, while the curvature terms will either cause two worldlines to either converge or diverge.