Do we 100% know what the geometry of the Universe is?

[PeterDonis]

Alan Guth's inflationary theory is the current leader of the field.

Inflation models don't necessarily eliminate the initial singularity.

 

[PeterDonis]

Obviously that's the problem, hmm. So we are in math world.

Newtonian physics is "math world" just as much as GR is. Newtonian physics is just different math, whose predictions are now known to not be as accurate as those of GR.

so that mean we are still finding what is really happening.

Depends on what you mean. We don't have good knowledge of what happened before the hot, dense, rapidly expanding state that we call the "Big Bang" (which is not the same thing as the "initial singularity" that appears in some models). We do, however, have good knowledge of the current spatial geometry of the universe--that it is flat to within a very good approximation (i.e., if it is actually curved, the radius of curvature is much, much larger than the radius of our observable universe).

So that mean all above members wrote in posts maybe is not 100% correct?

As has already been pointed out, we never can be certain that anything in science is "100% correct".

However, that is not the same as saying that we know nothing at all or that we don't know that the naive Newtonian model you have been implicitly using in your intuitions is not correct. We do know that that model is wrong, to an extremely high confidence: its predictions are nothing like what we see.

 

[Jaime Rudas]

In this context, flat is a technical term referring to the geometry of spacetime

And, specifically, to the geometry of space.

 

[PeterDonis]

flat is a technical term referring to the geometry of spacetime

And, specifically, to the geometry of space.

More precisely, to the geometry of spacelike hypersurfaces of constant FRW coordinate time (or, equivalently, constant proper time for comoving observers) in the overall FRW spacetime geometry.

 

[PAllen]

But how can this be physically possible?
Example with fluid, if you decrease distance between each molecule of air, shouldn't it come to one point?

Suppose simply that a current cosmological time state of the universe is unbounded Euclidean 3 space. Then every earlier state, however many doublings of density involved, is also unbounded. The cosmological time exactly zero is not actually part of the model (even in the idealized mathemetical model). Every time later than zero (even e.g. $1/(((10^{100})^{100})^{100})$ seconds after zero) is still an unbounded state. That is just the nature of infinity.

 

[Nugatory]

All stars/planets in universe lay at same plane as earth? How thick is this plane?

You are misunderstanding what “spatially flat” means. Intuitively it means that the Euclidean geometry works everywhere - the Pythagorean theorem is valid, parallel lines never intersect, the interior angles of a triangle add to 180 degrees, and so forth. The opposite of “flat” is “curved”.

It’s easy to visualize a three-dimensional flat space - we live in one, it’s the only three-dimension space we’ve ever known. It’s not so easy to visualize a three-dimensional curved space so we have to fall back on a two-dimensional analogy: the surface of a sheet of paper is two-dimensional and flat so Euclidean geometry works; the two-dimensional surface of the earth is not flat and Euclidean geometry doesn’t work (lines of longitude, initially parallel at the equator intersect at the poles, the interior angles of a triangle with two vertices on the equator and the third at a pole add to more than 180 degrees, and so forth).

 

[Drakkith]

But how can this be physically possible?
Example with fluid, if you decrease distance between each molecule of air, shouldn't it come to one point?

No, not if the fluid extends infinitely in all directions. In such a situation, as the distance between the molecules decreases, the density of the fluid approaches infinity everywhere while at the same time the volume always remains infinite.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

After moderator review, the thread will remain closed. Thanks to all who participated.