4
votes
1answer
144 views

Is the observable universe homeomorphic to $B^3$?

Is the observable universe homeomorphic to $B^3$? Where $$B^3=\{x\in \mathbb{R}^3 : |x|\leq 1 \}$$ Or is it even sensible to talk about space (rather than spacetime) as a 3 manifold?
1
vote
0answers
61 views

How to test that a flat metric represents a global three-torus geometry

When introducing Robertson-Walker metrics, Carroll's suggests that we consider our spacetime to be $R \times \Sigma$, where $R$ represents the time direction and $\Sigma$ is a maximally symmetric ...
0
votes
2answers
99 views

Does the universe have an edge/boundary/barrier? If yes, what is at the edge? [duplicate]

My question related kind of to asking what the shape of the universe is. Say a hypothetical alien civilization built an faster-than-light spaceship. If they keep flying would they end up where they ...
15
votes
3answers
1k views

Is topology of universe observable?

There is an idea that the geometry of physical space is not observable(i.e. it can't be fixed by mere observation). It was introduced by H. Poincare. In brief it says that we can formulate our ...
26
votes
4answers
3k views

Why does a flat universe imply an infinite universe?

This article claims that because the universe appears to be flat, it must be infinite. I've heard this idea mentioned in a few other places, but they never explain the reasoning at all.
7
votes
1answer
118 views

What is the concept of cosmic strings?

What is the concept of cosmic strings? Is it related to the strings in the string theory, and if it is, then how?
0
votes
0answers
53 views

General relativity and global aspects [duplicate]

The theory of general relativity tells me something about the global structure of space-time, eg simply connected ?
3
votes
2answers
320 views

Excluding big bang itself, does spacetime have a boundary?

My understanding of big bang cosmology and General Relativity is that both matter and spacetime emerged together (I'm not considering time zero where there was a singularity). Does this mean that ...
3
votes
2answers
351 views

(Co)homology of the universe

In this post let $U$ be the universe considered as a manifold. From what I gather we don't really have any firm evidence whether the universe is closed or open. The evidence seems to point towards it ...
1
vote
1answer
320 views

What is the fate of a 3-Torus universe?

Since it is flat, will it expand forever like a flat and open universe or collapse like a closed and curved universe?
2
votes
1answer
177 views

The topology of a “closed” universe - is it really closed?

The spatial part of the positive curvature FRW metric has the form \begin{equation} ds^2=\frac{dr^2}{1-(r/R)^2}+r^2d\Omega^2 \end{equation} or \begin{equation} ds^2=R^2(d\chi^2+\sin{\chi}^2d\Omega^2) ...
10
votes
4answers
1k views

Shape of the universe?

What is the exact shape of the universe? I know of the balloon analogy, and the bread with raisins in it. These clarify some points, like how the universe can have no centre, and how it can expand ...