I Did cosmic inflation happen everywhere in the Universe?

[JMz]

I don't get the 4-dimensional geometries thing. I majored in biology not physics.

Perfectly acceptable. But PF deals with the most mathematical science, and mathematical physics has existed for at least 100 years longer than mathematical bio has. We have a responsibility to look for common language with you, but it's not always possible to give you the extra 100 years of math background in an online forum. If you want to understand beyond the level of metaphors, as you seem to, then you have a responsibility to do some serious reading. We can suggest good sources.

 

[PeterDonis]

in the above multiverse picture, what is the black stuff, the stuff outside the bubble?

Meaningless. The response from @JLowe is correct.

The 'inflation field' resides in 'space', right?

It depends on which model of inflation you are talking about. In the "eternal inflation" model, which appears to be the closest one to the one you have in mind, the spacetime in which the inflation is occurring is separate from each of the "bubble universe" spacetimes that come into being. So from the viewpoint of any of those bubble universes, no, the inflaton field is not in their "space" (actually spacetime) at all. (More precisely, it doesn't have a nonzero value anywhere in their spacetime.)

 

[rootone]

Can you pls elaborate a bit further how 2 spacetime

There is not is not two spacetimes, who said that?

 

[PeterDonis]

There is not is not two spacetimes, who said that?

I think he was referring to a number of my posts in this thread. I was trying my best to express in ordinary language how an eternal inflation model can have multiple "bubble universes" that are spatially infinite (as we think ours is). Any attempt to describe this in ordinary language is going to distort something.

 

[rootone]

OK Peter. Thanks for the explanation.
Yes there are multiverse theories.
To be fair I need to sharpen my Occam's razor a bit.
and see a dentist as well.

 

[RobertSpencer]

Is Inflation a theory which is supported by lots of experimental evidence, or is it still a hypothesis?

 

[PeterDonis]

Is Inflation a theory which is supported by lots of experimental evidence, or is it still a hypothesis?

Both. We have evidence that our universe had an inflationary epoch (though not all cosmologists assign the same weight to it), but we don't have any real evidence for a multiverse or models like eternal inflation; discussion about the different possible inflation models are just theoretical at this point.

 

[RobertSpencer]

I think I am getting a little bit idea of what is going on.

Inflation's mathematical physics gives equations which shows that there can be bubble universe which are in different space-times.

Suppose there are 2 people in Bubble universe A and B, one in A and the other in B.

If A takes a spaceship and travels in any direction for any amount of time, you are saying that he will not meet the person in Bubble universe B.

So, this type of scenario is possible only if the 2 space-times are in 2 different dimensions I presume?

Are 2 4D spacetimes both having infinite space is a purely mathematical construct?

It's just on paper but no evidence exist for it?

Is it the maths that tells us that both can exist with infinite space in different space-times??

 

[PeroK]

I think I am getting a little bit idea of what is going on.

Inflation's mathematical physics gives equations which shows that there can be bubble universe which are in different space-times.

Suppose there are 2 people in Bubble universe A and B, one in A and the other in B.

If A takes a spaceship and travels in any direction for any amount of time, you are saying that he will not meet the person in Bubble universe B.

So, this type of scenario is possible only if the 2 space-times are in 2 different dimensions I presume?

Are 2 4D spacetimes both having infinite space is a purely mathematical construct?

It's just on paper but no evidence exist for it?

Is it the maths that tells us that both can exist with infinite space in different space-times??

Here's a different mathematical analogy. Suppose you are on the real number line. Given any positive number, if you go far enough to the right you will reach it. And, given any negative number, if you go far enough to the left you will reach it.

But, at what point do you encounter the function $f(x) = \sin x$?

The mathematical space of continuous functions is not connected to the number line, or to the space of 3D vectors. You could ask, if the space of 3D vectors takes up all of 3D space, then "where" are all these continuous functions? And, where is the set of nxn matrices? But, these are fruitless questions. Mathematically these sets of objects are separate. They belong in separate sets, each of which may be finite or infnite dimensional - the set of continuous functions is infinite dimensional.

You need to free up your mind a little. At the moment, it appears you cannot conceive anything outside a single 3D + 1T universe. There's almost no point in reading about multiverses if you can't think beyond this!

Try to imagine that there might be other universes with no spatial or temporal connection to our universe at all. Completely separate universes, with nothing in common with each other - not even the same laws of physics. As separate as the set of continuous functions is from the set of 3D vectors.

 

[jbriggs444]

2 space-times are in 2 different dimensions I presume?

The term "dimension" does not mean what you think it means.

 

[PeterDonis]

If A takes a spaceship and travels in any direction for any amount of time, you are saying that he will not meet the person in Bubble universe B.

That's correct.

his type of scenario is possible only if the 2 space-times are in 2 different dimensions I presume?

No, it just means the 2 spacetimes are not connected. In other words, when you say what you said in the first quote above, you've said all that needs to be said. There is no more.

It's just on paper but no evidence exist for it?

See post #57.

 

[nikkkom]

I can believe this. But PeterDonis says that those bubbles are spatially infinite.

Then we interpret the same pic differently. I see it as a depiction of inflationary model where more than one region of space underwent transition to the lower-energy vacuum.

 

[PeterDonis]

I see it as a depiction of inflationary model where more than one region of space underwent transition to the lower-energy vacuum.

Yes, but the "depiction" is obviously not accurate since it's not showing the "bubbles" of true vacuum as spatially infinite, whereas our best current model says the one we actually live in is spatially infinite.

 

[nikkkom]

Yes, but the "depiction" is obviously not accurate since it's not showing the "bubbles" of true vacuum as spatially infinite, whereas our best current model says the one we actually live in is spatially infinite.

I don't think so. Our observations only tell us that the size of our low-energy vacuum bubble is likely to be much bigger than observable Universe.

 

[PeterDonis]

Our observations only tell us that the size of our low-energy vacuum bubble is likely to be much bigger than observable Universe.

Our current best fit model is that our universe is spatially flat. That is based on combining a number of different observations. A 3-sphere with an extremely small curvature (so its 3-volume is much larger than that of our observable universe) is within the current margin of error, yes, but is considered unlikely.

However, the key point for this discussion is that, as far as I know, an "eternal inflation" model with multiple "bubble universes" is compatible with each bubble being spatially infinite. So whichever our own universe turns out to be, it would not rule out an "eternal inflation" model.

 

[nikkkom]

However, the key point for this discussion is that, as far as I know, an "eternal inflation" model with multiple "bubble universes" is compatible with each bubble being spatially infinite.

Well, this would only be possible if the Universe is more than 3-dimensional spatially, if it to contain infinite multiple 3-dimensional objects. I never heard that eternal inflation models assume that.

 

[PeterDonis]

this would only be possible if the Universe is more than 3-dimensional spatially, if it to contain infinite multiple 3-dimensional objects.

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.

 

[RobertSpencer]

Well, this would only be possible if the Universe is more than 3-dimensional spatially, if it to contain infinite multiple 3-dimensional objects. I never heard that eternal inflation models assume that.

I totally get this. This is talked about in Brian Greene's book Hidden Reality.

The only problem is, since that 4th spatial dimension is so small, I don't see how an entire universe can reside in it.

 

[PeroK]

I totally get this. This is talked about in Brian Greene's book Hidden Reality.

The only problem is, since that 4th spatial dimension is so small, I don't see how an entire universe can reside in it.

Perhaps it's a small universe!

 

[PeterDonis]

This is talked about in Brian Greene's book Hidden Reality.

Please note that this is a pop science book and you should not try to learn actual science from it. (Brian Greene's pop science books, in particular, seem to cause a lot of misunderstandings.)

 

[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.