In general relativity, we cannot determine the global structure of the universe (since it is not flat), therefore all measurements and observations are only meaningful locally. In particular, we can observe redshift of light from distant galaxies. And then we have the Expansion of the Universe described by Friedmann–Lemaître–Robertson–Walker metric explaining this redshift. However, I think there are always possibilities that different structures of universe may also give rise to this redshift. Is it true? Is there any kind of experiments that can help us determine the structure of the universe (or at least determine the universe is finite or not)?
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$\begingroup$ possible duplicate of Is topology of universe observable? $\endgroup$– ACuriousMind ♦Commented Jan 30, 2015 at 15:12
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$\begingroup$ @ACuriousMind It's not a duplicate of the linked question. That question is about measure the topology as in whether the universe is open closed or flat and the dimensionality. This is about if other types of fundamental geometries on the universe could give the same redshift results, what experiments might help us determine those geometries, or if an experiment can determine if the universe is finite or not. The other post wouldn't answer this because it assumes only an FLRW universe plus an infinite closed universe would look fundamentally the same as an infinite flat universe to us $\endgroup$– JimCommented Jan 30, 2015 at 15:18
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$\begingroup$ @Jim: I understand, and I think I agree with you. Duplicate vote retracted. $\endgroup$– ACuriousMind ♦Commented Jan 30, 2015 at 15:20
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$\begingroup$ @ACuriousMind BTW, great answer on the other question $\endgroup$– JimCommented Jan 30, 2015 at 15:20
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However, I think there are always possibilities that different structures of universe may also give rise to this redshift. Is it true?
The redshift is on average the same in every direction and depends on the distance, so if it came not from cosmic expansion but from "structure" (matter, energy distribution) that would mean that we were in the cosmic center because the farther from us the redder objects are, in every direction. Therefore the "structure" would have to increase its redshiftfavoring properties shellwise from our position. That is not very likely.
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$\begingroup$ @ [Jim][1] : That's right, with Doppler due motion IN space you get the Redshift as a function of velocity, while the FLRW redshift where you have a motion OF space is a function of the scale-factor. That means you have 2 velocities corresponding to the observed redshift: the one when the light was emitted, and the one when the light is observed. [1]: physics.stackexchange.com/users/23473/jim "profile" $\endgroup$– YukterezCommented Jan 30, 2015 at 19:50
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$\begingroup$ When I write structure, I mean different metric. $\endgroup$ Commented Jan 31, 2015 at 9:13