# Big crunch question

## Main Question or Discussion Point

I have a question regarding the big crunch, maybe a bit stupid, butI'm breaking my head over it. So the universe is expanding, we allagree on that one and we'd never be able to travel to the edge, end,call it whatever you want, because we cannot travel faster than lightand the universe is expanding a lot faster than that speed limit. Ok,I'm still gettin it, but now one theory is the Big crunch, and I'mkinda keen on that one, but what I don't get is... if it'scontracting, wouldn't we be able to reach the edge/end then? Anyone able to give me a simplefied answer on that one? Thanks a bunch...

Gold Member
... but now one theory is the Big crunch, and I'mkinda keen on that one, but what I don't get is... if it'scontracting, wouldn't we be able to reach the edge/end then?
Welcome to PF RikTammenaers.

The most important (< 1998) parameter in fate of the universe is the Density parameter, Omega (Ω), defined as the average matter density of the universe divided by a critical value of that density.

Omega (Ω) related to the curvature of space (global geometry, all forms of dark energy are ignored):

Ω > 1 positive curvature, spherical universe, Closed
Ω < 1 negative curvature, hyperbolic universe, Open
Ω = 1 zero curvature, flat universe, Flat

A closed universe (Ω > 1), lacking the repulsive effect of dark energy, gravity eventually stops the expansion of the universe, after which it starts to contract until all matter in the universe collapses to a final singularity, "Big Crunch". However, if the universe has a large amount of dark energy (as suggested by recent findings), then the expansion of the universe can continue forever.

An open universe (Ω < 1), even without dark energy, expands forever, with gravity barely slowing the rate of expansion. With dark energy, the expansion not only continues but accelerates. The ultimate fate of an open universe is either "Heat Death", "Big Freeze", or the "Big Rip".

In a flat universe (Ω = 1), average density of the universe exactly equals the critical density. Without dark energy, it expands forever but at a continually decelerating rate, approaching a fixed rate. With dark energy, the expansion rate of the universe initially slows down, due to the effect of gravity, but eventually increases. The ultimate fate of the universe is the same as an open universe.​

As you see it’s only the closed universe (Ω > 1) that can end in a final singularity ("Big Crunch"), and there is no edge on a sphere.

Even if a flat universe could "crunch", it doesn’t automatically have an edge – it could be compact in the shape of a torus.

I’m not sure, but I think that a flat universe that is not compact (torus), must be infinite... but maybe some of the pros could elaborate more around that...

Chalnoth
I’m not sure, but I think that a flat universe that is not compact (torus), must be infinite... but maybe some of the pros could elaborate more around that...
I think that the simple answer here is that we expect the curvature we measure in our part of the universe to be a local phenomenon, not a global one. Thus if the universe is much larger than our observable region, then a measurement of local curvature can't say anything about whether the overall universe is finite or not.

Gold Member
I think that the simple answer here is that we expect the curvature we measure in our part of the universe to be a local phenomenon, not a global one.
That’s very true. Like football fields that are perfectly flat (local geometry) – and still we know that the Earth is a sphere (global geometry).

But, doesn’t the local geometry put some constrain on the global geometry? (as described in http://en.wikipedia.org/wiki/Geometrization_conjecture" [Broken])

(... are there no 'hints' on the global geometry in the CMB ...?)

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Chalnoth
But, doesn’t the local geometry put some constrain on the global geometry? (as described in http://en.wikipedia.org/wiki/Geometrization_conjecture" [Broken])

(... are there no 'hints' on the global geometry in the CMB ...?)
The only thing we can say about the global geometry is that it doesn't wrap back on itself terribly quickly. If it did, we would see tremendous correlation between widely-separated points on the CMB, which we just don't see. It may wrap back on itself beyond our horizon, but this is by no means certain.

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George Jones
Staff Emeritus
Gold Member
I’m not sure, but I think that a flat universe that is not compact (torus), must be infinite..
Spatial hypersurface compactness/non-compactness is used as the definition closed/open universe.

As Chalnoth has noted, this is a global (not local) property. A topological space (in this case, a spatial hypersurface) is compact if any family of open sets that covers the whole space contains a subfamily that consists of a finite number of open sets which also cover the whole space.
But, doesn’t the local geometry put some constrain on the global geometry? (as described in http://en.wikipedia.org/wiki/Geometrization_conjecture" [Broken])
Take a look at the fascinating (for me) Chapter 15, Spatially Homogeneous Universe Models, from the book Einstein's General Theory of Relativity with Modern Applications in Cosmology by Gron and Hervik. Section 15.5, The 8 model geometries, discusses Thurston geometries; section 15.6, Constructing compact quotients, talks about universes that are locally the same, but globally different

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Gold Member
Thanks Chalnoth.

another question:

if the universe is flat like Krauss states, then am I right to assume that a big crunch is impossible? and only big rip or big freeze are? for me a big freeze doesn't fit the beautiful pattern of nature, everything co-exists perfectly,and then it would just all freeze and that's it, big rip I get, but does it mean that it all starts over a again with a new singularity?

Chalnoth
another question:

if the universe is flat like Krauss states, then am I right to assume that a big crunch is impossible? and only big rip or big freeze are? for me a big freeze doesn't fit the beautiful pattern of nature, everything co-exists perfectly,and then it would just all freeze and that's it, big rip I get, but does it mean that it all starts over a again with a new singularity?
Well, it's not the flatness, but rather the dark energy that makes a big crunch nearly impossible. Basically, we can't say that our universe is perfectly flat (such a thing is essentially impossible). But it is just incredibly flat. Now, if it just so happened that the dark energy was of a form that decayed away eventually, leaving a matter-dominated universe, then the curvature would tend to grow in its effect with time. Eventually whatever small curvature there is would become large, and if it was closed, even slightly, then it would eventually recollapse.

But for that to happen, the dark energy has to decay away first. I'm not aware of any reasonable dark energy models that actually do this, but theorists are quite creative, so there probably are a few out there somewhere.

George Jones
Staff Emeritus
Gold Member
another question:

if the universe is flat like Krauss states, then am I right to assume that a big crunch is impossible? and only big rip or big freeze are? for me a big freeze doesn't fit the beautiful pattern of nature, everything co-exists perfectly,and then it would just all freeze and that's it, big rip I get, but does it mean that it all starts over a again with a new singularity?
Nature doesn't like to have human preferences imposed upon it.

Here is one highly speculative way that a Big Crunch can occur for flat or negatively curved universes.

If the cosmological constant is not constant and becomes sufficiently negative in the future, then the cosmological "constant" can contribute to the attractive nature of gravity, and an open universe can collapse in a Big Crunch.

There is no observational evidence for this scenario.

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what do you believe in chalnoth? big bang is a fact, but what do you think is the outcome eventually, would appreciate your thoughts on this...

Chalnoth
what do you believe in chalnoth? big bang is a fact, but what do you think is the outcome eventually, would appreciate your thoughts on this...
Believe? It's not really a matter of belief as far as I'm concerned. But so far recollapse seems rather unlikely, due to the observation of accelerated expansion.

I really need to find dutch books :(

Gold Member
I really need to find dutch books :(
Start here http://nl.wikipedia.org/wiki/Heelal" [Broken]. I’ve learned more from Wikipedia than most popular science books. And the combination PF/Wikipedia is absolutely outstanding, in getting a chance to discuss a topic with a lot of very smart and well educated people.

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Gold Member
Constructing compact quotients, talks about universes that are locally the same, but globally different
This tells me two things:
1) It is not only QM that is 'magical'.
2) http://en.wikipedia.org/wiki/William_Thurston" [Broken] must have brains much much bigger than mine.

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Gold Member
... for me a big freeze doesn't fit the beautiful pattern of nature ...
Well, I think Chalnoth & George Jones answer the question. I just want to add that a "Big Crunch" will not be "beautiful" = hell in practice.

And furthermore, as I understand, there’s absolutely nothing that guarantees a recycling/regeneration of a "carbon copy" of our current universe in a "Big Bounce".

Depressing? Nooo, just enjoy the beautiful weather today, and consider that the sun will continue to shine for at least 5 billion years!

Well, I think Chalnoth & George Jones answer the question. I just want to add that a "Big Crunch" will not be "beautiful" = hell in practice.

And furthermore, as I understand, there’s absolutely nothing that guarantees a recycling/regeneration of a "carbon copy" of our current universe in a "Big Bounce".

Depressing? Nooo, just enjoy the beautiful weather today, and consider that the sun will continue to shine for at least 5 billion years!
lol :)

but i find it hard to believe that all would just cease to exist, it like has to be recycled and the multiverse theory i don't know, who knows maybe... pc wiki PF nice sources indead :) i'm also watching TTC (have like 50 vids) what's also a great source

Gold Member
... but i find it hard to believe that all would just cease to exist ...
Ask a newborn baby if it was hard not to exist a year ago? (maybe it’s safest to wait 2-3 years... )

You’re not the first one with this approach to the universe. Extremely intelligent Albert Einstein made his biggest blunder in assuming that the universe had to be eternal and static, therefore adding a positive cosmological constant to his equations of general relativity (that originally showed that the universe had to be either expanding or contracting).

Einstein didn’t believe in a personal God, more like the "lawful harmony of the world". The nature showed signs to Einstein that made him believe that there must be "something more" behind.

This was of course before Edwin Hubble showed that every galaxy is moving away from us, and Niels Bohr and Werner Heisenberg showed that the microscopic foundation of the world is a "randomized mess" that only can be handled with statistical probability distributions in the macroscopic world.

Einstein was not happy. This didn’t fit his idea of the "lawful harmony of the world". He accepted Edwin Hubble’s discovery immediately, but spent the rest of his life in an unfruitful struggle against the randomness of nature, stating – "God does not play dice with the universe".

What can we learn from this? Well, if one of the brightest men in the history made a big goof, just because he applied a human "philosophical property" on nature – which just wasn’t there – we better watch out, not to repeat the same mistake again.

(The interest for Einstein’s cosmological constant Λ is today renewed, since the discovery of cosmic acceleration in the 1990s.)

One striking example is colors. It’s very easy to think that the spectacular colors in nature just can’t be a result of a random evolution? But where are the colors? Well, in nature there are only different electromagnetic wavelengths, and the colors are only inside your head! And different animals see different colors/spectra...

I don’t want to spoil your next holiday, but this is the way it is.

P.S. Humans exists, the Universe just "evolve".

Chalnoth
lol :)

but i find it hard to believe that all would just cease to exist, it like has to be recycled and the multiverse theory i don't know, who knows maybe... pc wiki PF nice sources indead :) i'm also watching TTC (have like 50 vids) what's also a great source
Well, I think we expect that new regions of space-time would continually be born out of quantum vacuum fluctuations, but those regions will be forever cutoff from their parent universes. I rather like Sean Carroll's work in this area. He wrote a popular science article on the subject not long ago:
http://www.scientificamerican.com/article.cfm?id=the-cosmic-origins-of-times-arrow

Chronos
Gold Member
I second the quantum fluctuation hypothesis. Even if the universe is destined to suffer a 'heat death' it has a virtual eternity to reignite itself 'somewhere' in a blaze of glory. The 'old' universe will have long since faded beyond detectability. I am, in that sense, a fan of the eternal recycling universe, just not one with any umbilical [causal] connection to its 'mother'.

Gold Member
My opinion is that even if the human intellect have done gigantic and amazing progress in the understanding of the universe and nature – we might be "caught" forever in our "local bubble", starting ~400,000 years after BB, ending at the edge of the observable universe, 46.5 billion light-years away – never to get the "whole picture".

But stranger things have happened in science, so you never know!

Personally I don’t get this "worrying" about the final fate of the universe? If we are smarter than most of us think, and survive our own local "heat death", and Sarah Palin, and the end of the Sun, and manage to evacuate humankind to another planet/star – well, then almost anything else must be possible, including "tricking" the death of our local universe, right?

Gold Member
... I rather like Sean Carroll's work in this area. He wrote a popular science article on the subject not long ago:
http://www.scientificamerican.com/article.cfm?id=the-cosmic-origins-of-times-arrow
Sean is cool. In case there is any trouble accessing the link above, here’s a http://www.stealthskater.com/Documents/BigBang_05.pdf"