Curvature and inflation

[windy miller]

According to this paper, eternal inflation would be falsified by positive curvature:
http://arxiv.org/pdf/1203.6876v2.pdf
However the proposer of eternal inflation, Alex Vilenkin, has suggested spontaneous creation of the universe from"nothing". Apparently this doesn't violate the conservation of energy as i a closed universe the positive energy of matter is balanced by the negative energy of gravity. but as I understood it a closed universe has positive curvature which would rule out eternal inflation, wouldn't it? or why wouldn't it ?

 

[Chalnoth]

According to this paper, eternal inflation would be falsified by positive curvature:
http://arxiv.org/pdf/1203.6876v2.pdf
However the proposer of eternal inflation, Alex Vilenkin, has suggested spontaneous creation of the universe from"nothing". Apparently this doesn't violate the conservation of energy as i a closed universe the positive energy of matter is balanced by the negative energy of gravity. but as I understood it a closed universe has positive curvature which would rule out eternal inflation, wouldn't it? or why wouldn't it ?

Yes, a closed universe has positive curvature.

The "zero energy universe" isn't really something that makes a whole lot of difference. Energy is just not conserved in General Relativity. You can recover energy conservation only in very special circumstances, but there's no reason to believe that those circumstances apply to reality. Sean Carroll has a pretty good blog post on the subject:
http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

 

[windy miller]

Thanks for the quick reply, ok let's put energy conservation aside. Vilenkin claims his model of spontaneous creation from nothing needs a closed universe. See here: http://inference-review.com/article/the-beginning-of-the-universe
he also claims the universe undergoes eternal inflation. But the previous paper seems to say this would rule out eternal inflation. So it seems I have misunderstood something along the way.

 

[bapowell]

Why do you think that a closed universe is incompatible with future-eternal inflation?

 

[windy miller]

Because as I understand it a closed universe has positive curvature and according to papers like the one I cited above positive curvature would rule out eternal inflation.

 

[Chronos]

Eternal inflation, as I understand it, results in causally disconnected 'bubble' universes. I fail to grasp how the curvature in any particular 'bubble' universe could have any observable consequences in another causally disconnectes 'bubble' universe.

 

[bapowell]

Because as I understand it a closed universe has positive curvature and according to papers like the one I cited above positive curvature would rule out eternal inflation.

But the Guth et al. paper involves an observational constraint on positive curvature; Vilenkin's closed universe could still be viable as long as the observable patch is sufficiently flat (equivalently, the radius of the universe is sufficiently large).