Did cosmic inflation happen everywhere in the Universe?

[nikkkom]

You're making the same assumption @RobertSpencer is making: that all of the bubble universes need to be in the same "space". As I understand the "eternal inflation" models, that is not the case.

I'm very surprised. Eternal inflation models do not postulate any disjoint "spaces" or "spacetimes". They assume just the usual, single, exponentially expanding inflationary 3+1 dimensional spacetime.

 

[PeterDonis]

Eternal inflation models do not postulate any disjoint "spaces" or "spacetimes". They assume just the usual, single, exponentially expanding inflationary 3+1 dimensional spacetime.

Again, as I understand it, eternal inflation models allow for multiple "bubble universes" that are all spatially infinite. Do you agree? If not, can you give a reference that says otherwise?

If my understanding is correct, then, while it might be mathematically possible to construct a single 3+1 dimensional spacetime that contains all of the "bubble universes", it would not be the kind of model that @RobertSpencer is intuitively visualizing.

 

[kurros]

Again, as I understand it, eternal inflation models allow for multiple "bubble universes" that are all spatially infinite. Do you agree? If not, can you give a reference that says otherwise?

If my understanding is correct, then, while it might be mathematically possible to construct a single 3+1 dimensional spacetime that contains all of the "bubble universes", it would not be the kind of model that @RobertSpencer is intuitively visualizing.

I don't have a reference on hand, but I don't think you are correct. I don't remember ever reading anything about the "bubble universes" being spatially infinite. They *might as well* be infinite from the perspective of observers in them, because their "edge" is way beyond the Hubble horizon of any observers and therefore the edge is receding faster than light relative to all observers. So you can never get to the edge. But, if you take a spatial hypersurface, then there is indeed an edge to the bubble universe out there somewhere.

As for bubbles crashing into each other, this will essentially never happen because the spacetime between the bubbles is still undergoing inflation. Therefore all the bubble universes are receding away from each other at tremendous speed. The moment one is created it almost instantly finds itself completely isolated.

 

[JMz]

This is my understanding as well. However, that only comes (in my case) from pop-science accounts like the Universe TV series -- admittedly from professionals like Tyson and Michio Kaku, but it's not clear where the peer-reviewed parts leave off and the dramatic animation departs from that.

 

[PeterDonis]

I don't remember ever reading anything about the "bubble universes" being spatially infinite.

Our best current model of our own universe is that it is spatially infinite. If eternal inflation is true, then our universe is one of the "bubble universes". So if eternal inflation does not permit "bubble universes" to be spatially infinite, then either our best current model is wrong or eternal inflation cannot be true.

It is possible that our best current model is wrong in this respect; a spatially finite (3-sphere with extremely large radius of curvature) universe is still within the "error bars" of our observations, but the error bars keep getting smaller. Since eternal inflation models are still getting a lot of research effort, if they were really inconsistent with a spatially infinite universe I would expect to see the potential conflict between eternal inflation models and our best current model of our own universe discussed in the literature, and I haven't. That's why I have asked for references, to see if there are in fact such discussions in the literature that I am not aware of.

 

[Bandersnatch]

Our best current model of our own universe is that it is spatially infinite. If eternal inflation is true, then our universe is one of the "bubble universes". So if eternal inflation does not permit "bubble universes" to be spatially infinite, then either our best current model is wrong or eternal inflation cannot be true.

I'm just looking over (the talky parts of) Linde's 2007 paper on Inflationary Cosmology:
https://arxiv.org/pdf/0705.0164.pdf
He never refers to the nucleated bubbles as spatially infinite - only exponentially large domains in the larger inflationary landscape, merely causally separated from one another, and flattened. E.g. section 6 starting on page 15.

 

[Bandersnatch]

Here: https://arxiv.org/abs/0712.0571
I found another bit I can't really understand, but which seems to suggest that whether the bubbles are or aren't spatially infinite depends on how one foliates the space-time:

Inside the light-cone, spacelike surfaces of constant φ turn out, very interestingly, to also constitute (infinite) surfaces of constant negative curvature. Therefore, if these homogeneous surfaces are taken to be constant-time surfaces (as general relativity leaves us free to do), then they describe an open Friedmann-Robertson-Walker cosmology nestled inside the forward light cone, with metric
ds2=−c2 dτ2 + a(τ)2 [dξ2 + sinh2ξdΩ2]. (2)
The structure of a CDL bubble then looks entirely different depending upon how spacetime is ‘foliated’ into space and time. In the foliation outside that gives metric 1, the bubble is finite, non-uniform, and growing; in the foliation that gives metric 2, it is infinite and homogeneous.

 

[PeterDonis]

I found another bit I can't really understand, but which seems to suggest that whether the bubbles are or aren't spatially infinite depends on how one foliates the space-time

Yes, this is one of the very counterintuitive features of de Sitter spacetime, which is what describes the eternally inflating region. You can cut both finite and infinite spacelike slices out of the same 4-dimensional spacetime.

 

[Bandersnatch]

Right, but after reheating, when the bubble is no longer a de Sitter universe, we're forced back to the FLRW metric, right? We're no longer free to foliate as we please.
So, what would be the correct, or at least - least wrong - way of rendering this into words when talking about the inflationary multiverse?
That one can't even uniquely define finiteness of space prior to reheating, so the question is similarly meaningless to looking for conservation of energy at universal scales?

 

[PeterDonis]

after reheating, when the bubble is no longer a de Sitter universe, we're forced back to the FLRW metric, right?

Yes, you're right, inside a bubble universe the metric is no longer de Sitter (although with nonzero dark energy it will approach that at far future times).

We're no longer free to foliate as we please.

The FRW spacetime does have a "natural" foliation within itself, yes. But I think what the paper is saying is that this foliation (in which the spacelike surfaces are infinite) is not the same as the "natural" foliation you get if you look at the bubble as sitting inside the larger de Sitter spacetime. The latter foliation makes the region occupied by the FRW spacetime in each spacelike slice finite.

what would be the correct, or at least - least wrong - way of rendering this into words when talking about the inflationary multiverse?

The best I can come up with is basically what I've said previously in this thread, that "space" in an eternally inflating multiverse with lots of "bubble universes" in it doesn't work the way our normal intuitions would suggest.

 

[elcaro]

General Relativity equations tells us that the earliest time of the universe which our physics can tell us had infinite space and infinite density (i.e. matter).

Then space started expanding, thus increasing the distance of any 2 points of that infinite dense matter, thus making it less dense and eventually creating galaxies and stars.

So, the big bang which is really a big expansion happened everywhere in the universe.

So, then, cosmic inflation suggested by Alan Guth tries to give an explanation as to what caused the big bang (expansion).

So, my question is, did inflation happen everywhere in the universe, or did it happen only in the region (infinitely small region) which led to our observable universe?

So, my understanding is that at the earliest time our equations tells us there was infinite space and infinite matter density. Then in some places in that infinite space inflation happened creating bubble universes like ours, but in other areas the universe just expanded. So, somewhere in the infinite universe even now inflation can happen creating more bubble universes. This is called eternal inflation.

Is this the current model of the big bang with inflation added?

Then what is there outside the bubble universes?? More galaxies, or more of that infinite dense matter which did not go through inflation to create a bubble universe?

In the framework of eternal inflation, which by the way is eternal to the future, but not to the past (so it must have started a finite time ago) somewhere in the pre-existing pre-inflationary universe, some regions keep inflating, while in others inflation effectively ends giving rise to a new "bubble universe" like ours. So to your question to what is between these universes, the answer would be: inflating - that is exponentially fast expanding - space.

Eternal inflation can start in a small patch of the universe (we mean here, the universe as it existed before inflation started), so to your question wether or not inflation happened "everywhere" the answer is: not necessarily, as it could have started from a very small patch of space.

However, soon after eternal inflation starts, inflating spaces (as they grow exponentially fast) dominate volume wise over spaces where inflation did not start or has already ended. Our own "bubble universe" (note: we need to be carefull about naming things, since in the framework of the multiverse there are multiple universes like us, and to distinghuish them from the universe in the meaning of "all there is" we use the term "bubble universe") grew out of a small patch of inflating space, which for our observable universe started out the size of less then a proton to the size of a tennisball in around 10^-30 seconds. So for our "bubble universe" inflation occurred in all of the space of that bubble. But in some other portions of space, inflation never started, or inflation already ended (which then also formed into other "bubble universes").

Hope this clarifies the situation.