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.
0
votes
0answers
20 views

How did WMAP measure the flatness of space? [duplicate]

I read that WMAP constrained $\Omega_0$ to be $1$ within $1%$. I realize that the baryon acoustic oscillations will produce a preferred scale on the CMB. Knowing $H_0$ one could measure the angle of ...
5
votes
1answer
55 views

Open Big Bang-less universe?

This came up in discussion around a class I'm taking. For a Universe with $\Lambda$ and matter contributions to energy density (and implicitly curvature, but no radiation), can you have a universe ...
1
vote
3answers
129 views

Is the universe flat?

There are more than one way to view the description of the universe as flat. There is the description of an open, flat or closed universe in terms of it's fate, expansion forever away from gravity, or ...
2
votes
1answer
82 views

Size of the Universe: Curved vs flat? Finite vs infinite?

I have recently heard the theory that the Universe may be smaller than observed but may be curved to the extent that light rays may have looped past us once already and hence appear to have originated ...
19
votes
2answers
503 views

Why does dark energy produce positive space-time curvature?

My understanding is that dark energy, or equivalently a positive cosmological constant, is accelerating the expansion of the universe and I have read that this gives empty space-time positive ...
1
vote
1answer
239 views

What is the curvature of an empty universe?

My calculations tell me an empty universe has hyperbolic curvature. Is this correct? If it is, can anyone help me understand why this is intuitively?
1
vote
1answer
196 views

Ricci scalars for space and spacetime, local and global curvature

If Ricci scalar describes the full spacetime curvature, then what do we mean by $k=0,+1,-1$ being flat, positive and negative curved space? Is $k$ special version of a constant "3d-Ricci" scalar? ...
2
votes
2answers
198 views

What is the curvature of the universe?

What is currently the most plausible model of the universe regarding curvature, positive, negative or flat? (I'm sorry if the answer is already out there, but I just can't seem to find it...)
3
votes
2answers
679 views

Equation of the saddle-like surface with constant negative curvature?

What is the equation for the saddle-like 2d surface (embeded in 3d Euclidean space with cartesian coordinates x, y and z) with constant negative curvature frequently used to illustrate open universe ...
1
vote
2answers
258 views

How to concile flat spacetime and big bang?

After reading How do we resolve a flat spacetime and the cosmological principle? I still remain perplex. Please excuse my ignorance and try explaining to me : I thought that basically, when we ...
6
votes
1answer
217 views

Curvature of the Universe imaginary?

If the curvature of the universe is zero, then $$Ω = 1$$ and the Pythagorean Theorem is correct. If instead $$Ω> 1$$ there will be a positive curvature, and if $$Ω <1$$ there will be a negative ...
3
votes
2answers
264 views

asymptotic curvature of the universe and correlation with local curvature

There is not-so-rough evidence that at very large scale the universe is flat. However we see everywhere that there are local lumps of matter with positive curvature. So i have several questions ...