[pinballed (OP)]

Hi again.

I have understood that the universe is flat and has been so since the time of the cosmic background radiation.
Different measurements are confirming this.

The shape of universe is depending on density, Omega, which then is 1.

BUT; I believe that the density of universe has to have been higher before, with more of the energy compressed into
smaller space, and in the future the density should be lower.....

How can then universe have been flat, and be flat?

Thanks

[evan_au]

It would be better to say that the universe is flatish.

In parts of the universe like our Earth, Solar system and Galaxy, gravity distorts space so it is not flat.

Cosmologists are not interested in "local" effects like these, but are wondering about the overall shape of the universe - and it appears very close to being flat.

With the Nobel Prize being awarded for "dark energy causing the accelerating expansion of the universe", the theories may need to be tweaked, and it is possible that measurements we get from looking back in time (when gravity dominated dark energy) may be different from the measurements in the future (as dark energy is now more significant than gravity).

[pinballed (OP)]

Hi,

I heard a lecture where one of the measurements was checking the distance of spots in the cosmic background radiation,
and they measured exactly. Conclusion of this was that universe has been flat since that time - 400.000 years after big bang.
This is what puzzles me. Shouldn't be so.....


Magnus

[CliffordK]

There is even a Wikipedia page about the shape of the universe.  However, I seem to get lost with the arguments.

I think my definition of flat, and the cosmologist definition of flat may in fact be different.

When I think of flat, I think of something largely 2 dimensional, like a sheet of paper.

But, it appears as if the cosmologists have generalized that definition of flat to mean "not curved".  I.E.  any straight line in a 3 dimensional object is in fact straight.  So, it is not in fact, flat in a planar, 2 dimensional sense.  But, rather is generalized to a 3 dimensional (or more) sense.

[evan_au]

We have a saying that "the shortest distance between two points is a straight line". On a flat sheet of paper (as Euclid imagined geometry), there is only one such line. If you draw another line parallel to this line, it will never meet the first line, no matter how far you extend them.

However, a flat sheet of paper is not the only possible 2D shape - you could pick 2 points on the surface of the earth (roughly spherical) or on a horse saddle (roughly hyperbolic).

• On a sphere, any two parallel lines will eventually meet
• On a hyperboloid, it is possible to draw many parallel lines that never meet.

It is possible to extend these three 2D geometries to 3 (or more) dimensions. The shortest distance between two points is called a "geodesic", and you can do similar tests to the parallel lines test.

Current measurements say that the universe is close to being flat, but are not precise enough to exclude being slightly spherical or hyperbolic.

Some theories even speculate that the universe has more than 3 dimensions of space, but these "extra"dimensions are "rolled up"  like a cylinder. So some dimensions could be spherical/cylindrical, while others are hyperbolic... These theories try to explain why gravity is so much weaker than the other fundamental forces.

[CZARCAR]

whats the black hole theory of the universe?

[pinballed (OP)]

Hmmm....Guess you know the answer (I know what I can read) but I get curious why you ask...?

[yor_on]

Magnus, are you thinking that with a higher 'energy density' there should be a curved universe? And as the density versus distances becomes 'diluted' the universe 'straightens out' giving it a 'flat' appearance? As a byside, I think Evans description capture rather well how cosmologists describe that 'flatness'. The question is about how those 'parallel lines' will behave as I understands it. Do they diverge? Close in on each other? Or do they stay parallel. In a 'perfectly flat universe' they should stay the same as I expect. So, for those finding this flatness a weird idea it's not about our three dimensional space flattening out into a nothingness, it's about the overall 'shape' of our universe instead. As long as there is gravity we will have a three dimensional 'space' as I think, even though we might define ourselves as 'freefalling', and so without gravity existent locally.

Also it doesn't exclude the possibility of the universe folding in on itself as I understand?
Like going out to right, simultaneously coming in from the left.

This one describes both ideas understandably.
=

To expand a little on those 'parallel lines'. One need to remember that they are depicted inside a universe, to draw parallel lines never meeting on the outside of a ball is not difficult, but imagine them starting inside instead, at the south side going to the north, well, sort of As they do so they will have to adapt to the 'shape' of that ball and at some point they should be destined to meet, as the balls geometry 'forces' them together. All as I think of it. Don't know if that one makes much sense though as I reread myself.. Better check the link above to see it.

[yor_on]

Are you thinking of N. J. Poplawski, Czarcar?
Cosmology with torsion: An alternative to cosmic inflation.   

[yor_on]

I needed to refresh my understanding here as I got stuck on the 'critical density' factor for those parallel lines.

It has to do with the Big Bang, and how those lines looked at that point in time. To stay so perfectly balanced between a negative and positive curvature of our SpaceTime, meaning keeping those lines so parallel one would need that original BB to be inside a very narrow window. To large a deviation from that window would end in totally different universes, a little like shooting a arrow at some target far away. And that's a weird thing to notice, why would it be that way?

The other is called the horizon problem. Why does the universe look the same in all directions? if two places are so displaced from each other that light, as information, can't have reached between them in the time this universe has existed, according to main stream definitions, how can both be equivalent,  homogeneous and isotropic? And that includes their temperatures as well as the natural background radiation measured.

And that is what the inflation and subsequent expansion propose to solve. There you have a inflationary period in where there is no 'center', instead it grows from all points existing, and as it ads more points it just keeps on growing from them too. But to make it untraceable to some original point one also will have to assume that there was no 'linear procession' to it, and that 'they' somehow(?) just appeared all over, meaning that a normal causality chain can't have been existent there. I don't know what to think about that? It depends on what 'time' is, as a guess and 'interactions' as this definitely was some sort of interaction.
=

When it comes to the density we can't use that alone though, Einstein created the cosmological constant to define a static universe. Without something counterbalancing gravity, with all mass attracting all other mass, the universe should fall together. Later he changed his mind there as the expansion was found existing, and dark matter was introduced as one explanation. But dark matter isn't enough for explaining why the universe is flat, and that's where we introduce dark energy. Or, just use Einsteins cosmological constant as a 'counter balance'. It is also there the discussion of 'vacuum energy' comes in from QM. But the theoretical QM definition of that vacuum energy is about 10¹²⁰ times too large, making it impossible as an explanation as yet.

[yor_on]

Hawking and Jim Hartle had this idea though that you might be able to use QM and statistics to define a Big Bang. And then the universe becomes a question of 'sum over histories' in where the universe could be assumed to have a 'no boundaries condition' included that allowed it to 'exist' always. Take a look at http://www.ralentz.com/old/astro/hawking-1.html

I don't know? The Big Bang is a mystery to me, either it introduces degrees of freedom (dimensions) from 'nothing', at least from the point of view of where we measure in? Or the universe are something 'limited' created out from, or inside, something 'more'. Then you have Smolin's ideas (loop quantum gravity) and string theory in where it all becomes a puzzle. And if we use Black Holes/White Holes you create a condition in where you have to assume a endless procession of them, as I can't see any 'origin' to them, not without another Black Hole predefined, add infinitum, giving 'birth' to the new SpaceTime/White Hole.

I guess that's what Hawking and Jim Hartle tried to get around
Time.