Is the Universe Finite? Exploring Expansion and Existence | True or False?

[Stephen_Ceci]

False. We cannot conclude anything about the size/shape of the universe based on our current knowledge, other than that it is likely to be FAR bigger than the Observable Universe. It could be infinite or it could be finite but unbounded.

Finite but unbounded can happen in infinite dimensional spaces. However, in finite dimensional spaces unboundedness seems incompatible with finiteness. Can you explain this further?

 

[weirdoguy]

However, in finite dimensional spaces unboundedness seems incompatible with finiteness.

Why? Think about 2D sphere.

 

[Bandersnatch]

Finite but unbounded can happen in infinite dimensional spaces. However, in finite dimensional spaces unboundedness seems incompatible with finiteness. Can you explain this further?

phinds means without boundary when he says unbounded. I've been trying to get him to use the terminology correctly for ages

Why? Think about 2D sphere.

The surface of a 2D sphere is bounded. It does not have a boundary.

 

[phinds]

phinds means without boundary when he says unbounded. I've been trying to get him to use the terminology correctly for ages

AAACCCKKKK ! I'll never learn apparently. Thanks and sorry.

 

[Stephen_Ceci]

By bounded I am just thinking simple metric spaces where distances in space or space-time are finite. Can you explain how a distance would be infinite in such a space?

 

[PeterDonis]

I had had the same impression that you did, which was that the Big Bang Theory started immediately after the singularity but Peter told me that it is not considered to have started until after the tiny part of the first second which is the inflationary period.

More precisely, the first state of the universe that we actually have good observational evidence for is the hot, dense, rapidly expanding state that, according to our best current models, occurred at the end of inflation. This state is the one that is properly referred to as the "Big Bang" state in our actual cosmological theories--the term "Big Bang" is also used to refer to those theories themselves, the group of models that all contain the same hot, dense, rapidly expanding state and the same future development of that state into the universe we observe.

In articles for non-scientists, it is true that the term "Big Bang" is also used to refer to the "initial singularity" that appears in highly idealized models such as those that were developed in the 1920s as the first attempts to apply General Relativity to cosmology. However, practically nobody actually believes that those models are applicable before the end of inflation, i.e., before the "Big Bang" state described above. They are just notional models that are used to get across some basic ideas to non-scientists. (There are some speculative models that try to extrapolate the highly idealized models back to the Planck epoch, but AFAIK they haven't gotten any traction.)

Also, while our best current understanding is that what preceded the "Big Bang" state described above was an inflationary epoch, we actually don't know that with the same confidence that we know about the "Big Bang" state itself. It is possible that something else came before, and there are various speculative models that have been published in the literature. But they all have in common the key property that there is no "initial singularity". In inflationary models, the inflationary state is "eternal" in the past (some early inflation models weren't like this, but those have all been ruled out). In other speculative models, there are various versions of a "bounce", i.e., a previous collapse phase that got turned by some quantum process into the expanding phase we now observe. There is even a speculative model (the Hartle-Hawking "no boundary" proposal) in which the universe only has a finite extent in the past, but there is no initial singularity (quantum corrections "smooth things out" so that everything remains finite--yes, it's counterintuitive, but AFAIK nobody has challenged the mathematical consistency of this model).

In short, there is no current version of a "Big Bang theory", whether it's our best current understanding or the speculative alternatives, in which the theory starts "immediately after the singularity". The only model in which that is the case is the notional model described above, that nobody actually believes is applicable. That's why I objected to that particular phraseology.

When ever someone disagrees with a published article and does not offer a competing publication I really don't give their opinion much credence.

Your "published article" is not a textbook or peer-reviewed paper; it is just an article for popular consumption on the NASA website. (At least, that's the "published article" you linked to in the exchange with phinds that led to this post by me.) You should not be using it as a source to find out what the Big Bang theory, the actual one used by cosmologists and described in textbooks and peer-reviewed papers, actually says.

If you want something from an actual paper, the Liddle paper that was linked to earlier has this on p. 10:

"Inflation does not replace the hot big bang theory; it is a bolt-on accessory attached at early times to improve the performance of the theory."

In other words, the inflationary epoch happened before the events covered by the standard hot big bang theory. This is entirely consistent with what I described earlier in this post. Note also that that paper never even mentions an "initial singularity".

 

[Pjpic]

I think that the following article, "Misconceptions about the Big Bang, Scientific American Feb 21 2005. by Charles Lineweaver and Tamara Davis world be of interest.

http://ccs.dogpile.com/ClickHandler.ashx?encp=ld%3d20160719%26app%3d1%26c%3dinfo.dogpl%26s%3dDogpile%26rc%3dinfo.dogpl%26dc%3d%26euip%3d174.109.107.219%26pvaid%3dd4b0380c60e7485f91fe0baa30eef7b3%26dt%3dDesktop%26sid%3d1830193568.760267776997.1468940139%26vid%3d1830193568.760267776997.1373747654.118%26fcoi%3d417%26fcop%3dtopnav%26fct.uid%3d30e880645d4c4e599ca2d928badf81bf%26fpid%3d27%26en%3d0WEFU%252fZhSoTF%252fFm%252bpLeuVl4UPZzISdzyg%252baGYj7N8ISb7M1aTnzzgA%253d%253d%26ru%3dhttp%253a%252f%252fwww.mso.anu.edu.au%252f%25257Echarley%252fpapers%252fLineweaverDavisSciAm.pdf%26ap%3d2%26coi%3d1494%26npp%3d2%26p%3d0%26pp%3d0%26mid%3d9%26ep%3d2%26du%3dwww.mso.anu.edu.au%252f%257echarley%252fpapers%252fLineweaverDavisSciAm.pdf%26hash%3d92C2CD1E7C9BBAB63BB27317AA86EB09&cop=main-title

This is a very readable article that directly addresses pretty much everything that has been kicked around on this thread.
Highly recommended.

--diogenesNY

The second series of pictures on page 39 suggests (to me anyway) that the big bang has a boundary that is displacing the white space. But I don't think that is correct for some reason.

 

[Sue Rich]

It's a major theory that space can be bent. If that's the case, wouldn't that make our universe finite?

 

[Quantum321]

It's a major theory that space can be bent. If that's the case, wouldn't that make our universe finite?

[1] Measurements indicate that the universe is flat, suggesting that it is also infinite in size. (however this is still being debated) The speed of light limits us to viewing the volume of the universe visible since the Big Bang; because the universe is approximately 13.8 billion years old, scientists can only see 13.8 billion light-years from Earth. [Infographic: The History & Structure of the Universe]

1. http://www.space.com/24309-shape-of-the-universe.html

 

[phinds]

It's a major theory that space can be bent. If that's the case, wouldn't that make our universe finite?

No, it is NOT a major theory that space can be bent. That is a pop-sci misconception. Space is not a thing that can be bent or stretched.

This misconception comes about because in space-time, absent any force, an object follows a geodesic, which in Riemann Geomtry (the geometry that describes space-time) is a straight line. In Euclidean geometry, which is not actually applicable, these space-time geodesics appear "bent".

How you conclude that this requires a finitely universe, I have no idea but it does not.

 

[PeterDonis]

It's a major theory that space can be bent.

I assume you are referring here to GR. GR says that spacetime can be curved (and is if gravity is present). But that does not require "space" to be curved. "Space" is not an invariant concept; it depends on your choice of coordinates. So saying "space can be bent" is not really a statement about physics; it's a statement about a particular coordinate choice. Choices of coordinates can't affect the underlying geometry of spacetime, so they can't affect whether the universe is finite or infinite.

 

[PeterDonis]

Now that the poster who gave incorrect references about the "standard Big Bang model" is gone, in case anyone else is interested, the actual "standard model" of Big Bang cosmology is described here...

https://en.wikipedia.org/wiki/Lambda-CDM_model

...and in the references given there.

 

[phinds]

Peter, thanks for your clarifications on all this.