A Closed Timelike Universe

[ydoaPs]

The typical answers for the shape of the universe are positive curvature, flat, and negative curvature. Is it possible that the curvature could be such that the entire universe is one closed timelike curve? One such that the Big Bang is caused by the Big Crunch? I'm not talking about a cylical model, but one where the end event and the beginning event are in fact the same event.

 

What would we need to look for to falsify this idea?

[elfmotat]

In the FLRW metric (which you seem to be speaking of), no, though you may find the Godel metric of interest: http://en.wikipedia.org/wiki/Gödel_metric.

[ydoaPs]

Is there a possible solution where there's a slight curvature and the universe is so big that the curvature ends up being a CTC?

[elfmotat]

I don't think so, at least not to my knowledge. All of the solutions I've seen with CTC's involve some sort of rotation or cylindrical symmetry. For example:

 

http://en.wikipedia.org/wiki/Kerr_metric (its interior contains CTC's)

http://en.wikipedia.org/wiki/Van_Stockum_dust

http://en.wikipedia.org/wiki/G%C3%B6del_metric

http://en.wikipedia.org/wiki/Tipler_cylinder

Edited May 2, 2012 by elfmotat

[michel123456]

The typical answers for the shape of the universe are positive curvature, flat, and negative curvature. Is it possible that the curvature could be such that the entire universe is one closed timelike curve? One such that the Big Bang is caused by the Big Crunch? I'm not talking about a cylical model, but one where the end event and the beginning event are in fact the same event.

 

What would we need to look for to falsify this idea?

 

That's a bit tricky but that's not a bad idea.

To falsify we should inquire information from the future, since the end (in our future) would be the same event that what we observe in our past (the BB). I am not sure it is possible to gather information from our future.

 

Also the universe would show full time symmetry, I guess.

And our mathematical model of the future of the universe would produce a Big Bang. I guess again.

[Royston]

The typical answers for the shape of the universe are positive curvature, flat, and negative curvature. Is it possible that the curvature could be such that the entire universe is one closed timelike curve? One such that the Big Bang is caused by the Big Crunch? I'm not talking about a cylical model, but one where the end event and the beginning event are in fact the same event.

 

What would we need to look for to falsify this idea?

 

I actually asked the same question when I studied cosmology a couple of years back. I'm pretty sure CMBA (cosmic microwave background anisotropies) rule this out, due to not agreeing with (as elfmotat stated) rotational models. They don't fit CMB data. It maybe worth looking into Bianchi cosmological models, as further rotational models have been built from these, IIRC Hawking proposed a rotational model built on one of the many Bianchi classifications. This is from memory, so I'll dig up some links.

 

This is very high end cosmology though, and probably won't make sense unless you have an understanding of Lie algebra. Point being, there have been more advanced models after the Godel metric, but I'm pretty sure they've been rejected.

 

EDIT: I think I should have mentioned I don't understand Lie algebra...I've only studied and understood basic solutions to GR

Edited May 2, 2012 by Royston