# Flatness of the Universe

1. Mar 23, 2014

### mannygonzales1

Hi, I was just wondering if someone could explain to me in detail what cosmologists mean when they say "the universe is flat."

To my understanding it is the geometry and topology of the universe they are referring too. But is space itself a sphere? And everything inside space is geometrically flat and infinite?

Thank you for explaining.

2. Mar 23, 2014

### Cosmobrain

Excellent question. I hate the fact they call the Universe flat, spherical or hyperbolic. What they mean is that the Universe would be flat if it had two dimensions. If you fire two beams of light and they travel parallel to each other, they will remain that way forever. If the Universe was open, they would eventually diverge. Someone else will explain this better because I can't get my head around this.

cb

3. Mar 24, 2014

### Chalnoth

It's "flat" in that if you take a constant-time slicing of the universe, that slice is composed of flat space. That is, if you build triangles by holding three points of a loop of string so that the three edges are taut, the angles of that triangle will always add up to 180 degrees, no matter how large the triangle.

By contrast, if you do the same thing across the surface of the Earth (holding the string flat across the surface and pulling it tight), you won't get 180 degrees. For a triangle that stretches from the equator to the north pole and back to the equator 90 degrees from the starting point, the sum of the angles is 270 degrees.

4. Mar 24, 2014

### julcab12

..EDIT: 2 different ways in describing flat. (1) Mentioned by Chalnoth, where the geometry of the universe in a parallel lines will never cross, the angles in a triangle will always add up to 180 degress, and the corners of cubes will always make right angles(Euclidean geometry). When they try to measure the baryon acoustic oscillations — waves of particles and energy(baryon wave as ruler). It came to almost flat or 'consistent' to flat(conservative type^^). (2)... The other 'flat' came from the prediction of the theoretical inflation theory - energy density of the universe was dominated by something with an equation of state approximating that of vacuum energy, p < - (1/3)p that eventually drives the universe toward a flat (Omega = 1). There is a growing interest in Inflation side (due to latest result; B-mode polarization) but will see.

Last edited: Mar 24, 2014
5. Mar 24, 2014

### Chalnoth

Those aren't different meanings. They're just different ways to describe it.

6. Mar 24, 2014

### julcab12

Yes. My bad. Done editing. Thanks for the correction. ^^

7. Mar 24, 2014

### mannygonzales1

So I'd like to ask a question that generally gets me confused, so if one could clarify it for me that would be great.

The universe is flat, in the sense of geometry and topology, so when physicists refer to there being more universes, they refer to them as being bubbles as well as ours. Is space spherical? Is the universe spherical? Or is everything flat?

8. Mar 24, 2014

### Chalnoth

When people are talking about "bubbles" they're not talking about geometry. They're talking about the idea that some parts of the universe are disconnected in some sense from other parts.

9. Mar 24, 2014

### phinds

"Bubble universes" are totally unproven, so I'm not sure that everyone who talks about them means the same thing. I personally don't believe in them, but that is an opinion with no facts to back it up, just based on the LACK of facts on the other side of what seems to me to be an unnecessarily complex picture.

Space is NOT spherical. The "bubble" is more like the term "quarter", as used when specifying a region of Paris. It doesn't mean 1/4th the way we normally think of "quarter" meaning, it just means "area". Likewise, "bubble" mean something more like "region".

10. Mar 24, 2014

### mannygonzales1

So the ACTUAL shape of the universe is flat? Don't mean to bombard with questions.

11. Mar 24, 2014

### phinds

As you may be aware, mass "warps" or "bends" spacetime. This is how the theory of General Relativity was proven, by looking at what seemed like "curved" beams of light from distance stars as it passed our sun during a solar eclipse. There is a famous saying that is a good way to think about the "warping":
So, it is established that mass bends spacetime. But how about if you get out in a region of space that is as far as possible from all mass (and that can be QUITE far)? Is there anything else that "bends" spacetime? Well not so much that there is something that bends it but rather that a "bend" is part of its characteristics. By "bend", I mean in reference to a Euclidean line. Light around a large mass does not follow a Euclidean line, it "bends" relative to one.

Space ITSELF can have a topology that has a built-in "bend" in this sense. If it does not have such a bend, it is said to be flat. As has been pointed out, if it causes two Euclidean lines to diverge, then it is said to be "open" and if causes them to meet, it is said to be "closed".

It is not known that our universe is flat, but it has been measured as being flat to within something like 3% (I may be a bit off on that and it's probably known to be closer than that now).

12. Mar 24, 2014

### Chalnoth

The question, worded that way, isn't quite specific enough. There are two different aspects of shape:
1. The local curvature.
2. The overall connectedness.

The first is what we mean when we say, "space is flat." The second goes under the name of "topology" and may take some explaining.

In topology, a cube with rounded corners and a sphere are the same thing: you can transform one into the other by stretching and bending without any kinking or tearing.

But a donut is entirely different: you can't transform a donut into a sphere without tearing.

As of right now, what we know is that the observable universe is extremely close to flat in terms of the local curvature. This could mean that our observable universe is just a tiny slice of a gigantic spherical topology, large enough that we can't measure the spherical curvature. It could mean that the observable universe is part of a torus (which doesn't have any overall curvature). Or it might be some other topology altogether. Right now, we just don't know what the overall topology of our universe is, because the observable piece is only a small part of it.

13. Mar 24, 2014

### mannygonzales1

Thank you. Using what you said, is it correct to come to the conclusion that the topology of the universe isn't quite known but the geometry has been found to be flat or a Euclidean Geometry?

14. Mar 24, 2014

### Bill_K

WMAP says:

"We now know (as of 2013) that the universe is flat with only a 0.4% margin of error."

What they mean when they say 'flat to within X percent' is that the total observed density (baryons + dark matter + dark energy) equals the critical density to within X percent.

Last edited: Mar 24, 2014
15. Mar 24, 2014

### Chalnoth

....which is another way to say that the total energy density equals the square of the expansion rate to within that level of accuracy (with a constant conversion factor of $8\pi G/3$).

16. Apr 12, 2014

### billyalex2

Let me throw my 2 cents in. Sometimes a certain explanation will just ring true for different people. When i think about the flatness of the universe i try not to think of it as existing either as a sphere or a small cube in an otherwise gargantuan sphere, which may actually be what we live in. I think of Einsteins curvature of space-time due to gravity. Since mass warps space-time into various "shapes" this causes space to curve in on itself. For example the milky way rests in a very large curved region which is not flat and two parallel lines beginning at one end will no longer be parallel at the other due to the warping that all the matter and energy causes as they traverse the galaxy. So think of the milky way as a gigantic, very curved space-time region. It is VERY hard for anything to escape its gravity well due to its curvature. Well just as a region of space, like the milky way can be curved so can the entire observable universe when observed as a whole. However when we look at the entire observable universe there appears to be no overall curvature. The density of matter and energy is too small to create an overall curvature. It looks flat. So in theory two parallel lines will not converge, however in reality they will bend and converge/diverge as they travel through both gravity wells and voids. This is why we observe gravitational lensing. The light from behind massive clusters is bent and converges towards our telescopes. Those lines are not parallel. But on the largest of views space-time shows virtually no curvature and parallel lines never converge or diverge. This is how i think when i think of space-time being "flat". It doesnt necessarily mean we live in a gigantic sphere. I think that question has more to do with whether the universe is finite or infinite which is a different but related question. I think. Any thoughts from anyone? Thanks