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Many apologies for this OP as I'm sure it has been raised many times before. 

IFF the universe were truly infinite in spatial extent (and I appreciate the 'unknowability' aspect of this), would this imply perforce that whatever the energy density of the earliest moments of the universe, it too would have been spatially infinite?

In such circumstances, would GR predict gravitational effects to be compressive, tensile or ... just undefined.?

 

Edited by sethoflagos
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5 hours ago, sethoflagos said:

IFF the universe were truly infinite in spatial extent (and I appreciate the 'unknowability' aspect of this), would this imply perforce that whatever the energy density of the earliest moments of the universe, it too would have been spatially infinite?

I don’t fully understand the question - what do you mean by energy density being “spatially infinite”?

In general terms, we need to distinguish between local geometry, and global topology of the universe. When we say that the universe expands, what that actually means, in general terms, is that measurements of spatial distances are dependent on when they are made; so if you pick two arbitrary (not gravitationally bound, and at relative rest) points in space, and measure their separation (e.g.) 10 million years after the BB, and then again 10 billion years later, you will get a different result, even though you are using the same pair of points, and the same ruler. That’s geometry.

The global topology roughly speaking tells you something about the overall “shape” of the universe - it is constrained, but not necessarily uniquely determined, by local geometry. It also doesn’t change - if the universe had a certain topology at the beginning, it will still have that same topology later on.

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6 hours ago, Markus Hanke said:

I don’t fully understand the question - what do you mean by energy density being “spatially infinite”?

I meant the necessity of the early universe itself being spatially infinite in this case as opposed to a (near) pointlike spatial singularity.

   

 

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5 hours ago, sethoflagos said:

I meant the necessity of the early universe itself being spatially infinite in this case as opposed to a (near) pointlike spatial singularity.

   

 

This is now rather dated [1998] but I assume it still holds scientifically true...The BB applies to the  "observable"  universe.

http://www.astro.ucla.edu/~wright/infpoint.html

 

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17 hours ago, sethoflagos said:

I meant the necessity of the early universe itself being spatially infinite in this case as opposed to a (near) pointlike spatial singularity.

   

 

Again, this essentially comes down to the difference between topology and geometry. When we say the universe is spatially infinite, what we actually mean by this are three things:

1. Spacetime has no boundary
2. For any arbitrary pair of (spatial) points {A,B}, there exists another pair of points {C,D} the spatial separation of which is greater than that of {A,B}.
3. Spacetime is singly connected

Herein, (2) actually implies (1), but I’m listing them separately for added clarity. These three conditions are true at all times t>0, including immediately after the BB, and at the present time; so this does not change, and it - roughly - represents an aspect of the global topology of the universe.

On the other hand, when we say that the universe was singular at the BB, what we mean is that as t -> 0, the separation between any pair of arbitrarily chosen spatial points will tend towards zero; and it means that no geodesics can be extended beyond the hyperslice t=0, without them extending into the future again (so this is a bit like a “pole” in spacetime). It does not really mean - at the danger of straying into the disciplines of metaphysics and philosophy here - that only a single point existed; the spacetime manifold was already there in some sense, but there was no notion of “separation between events” yet. So it’s the geometry that was singular, but not necessarily the topology.

Of course, this is the purely classical picture, it does not account for any quantum effects (which will likely change the story quite radically).

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So in this viewpoint, there is no preferred (spatial) direction for any of the forces at play here.

I was going to proceed to my follow-up question of what happens (to us) when there's no preferred direction for gravitational forces. But I'm now getting the feeling that you've already answered that. In that it's not about 'us' - it's about how mass acts on spacetime. And we're just little specks riding on that ebb and flow. Humbling thought. Thank you once again, Markus. 

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16 hours ago, sethoflagos said:

So in this viewpoint, there is no preferred (spatial) direction for any of the forces at play here.

Indeed not. The cosmological model we are using (the Lambda-CDM model) is, at large scales, based on homogeneity and isotropy.

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