Question on paper: Inflationary spacetimes are not past-complete

[Lynch101]

TL;DR Summary

Is the below summation an accurate representation of the peer reviewed paper?

Firstly, it might be worth asking if anyone is familiar with the above paper entitled 'Inflationary spacetimes are not past-complete' by Arvind Borde, Alan H. Guth, Alexander Vilenkin? If you are, you might be able to help me with this question.

I was doing some reading trying to get a better understanding of 'the big bang' and a thread on here led me to an article on Forbes. I know pop-sci articles are not a good source of information but the article links to a peer reviewed paper* entitled 'Inflationary spacetimes are not past-complete'. I'm wondering if the emboldened comment from the author of the Forbes article is an accurate deduction from the paper.
Bold added by me.

There is a theorem, famous among cosmologists, showing that an inflationary state is past-timelike-incomplete. What this means, explicitly, is that if you have any particles that exist in an inflating Universe, they will eventually meet if you extrapolate back in time. This doesn't, however, mean that there must have been a singularity, but rather that inflation doesn't describe everything that occurred in the history of the Universe, like its birth. We also know, for example, that inflation cannot arise from a singular state, because an inflating region must always begin from a finite size.

Forbes Article

If you are not familiar with the paper, is there perhaps additional information that I could provide that might be helpful? I'm not sure myself, but if there were something in particular you could suggest, I can take a look in the article.*At least I think it's peer reviewed.

 

[phinds]

The bolded statement is true if you posit a model that simply extrapolates back in time w/ no other consideration, AND if you are positing a model that does not allow for an infinite universe, BUT ... the current model of cosmology, the Big Bang Theory, breaks both of those. It only allows extrapolation back to the end of the inflationary period at which time the universe may have been infinite but in any case is not such that all particles would be on top of each other and of course it does allow for an infinite universe.

 

[Bandersnatch]

@phinds, you're talking about BB. The topic is specifically about inflation. I.e. that thing you tack on to the naive BB model at the early stages to (among other things) get rid of the singularity, also has a singularity. With the conclusion that maybe we need to duct tape something else at the early stages of inflation too.

Also, the bolded statement is a half-truth in either case, as rolling back the time causes all points to causally separate. That is to say, while they get infinitely close in the limit, they never 'meet'. The closer they get, the less time there is for signals to propagate. The isolated points, at least some of them, only begin to meet as expansion (inflationary or regular) progresses and they are able to exchange signals. But the nuance will likely be lost on a casual reader, so meh.

 

[Lynch101]

The bolded statement is true if you posit a model that simply extrapolates back in time w/ no other consideration, AND if you are positing a model that does not allow for an infinite universe, BUT ... the current model of cosmology, the Big Bang Theory, breaks both of those. It only allows extrapolation back to the end of the inflationary period at which time the universe may have been infinite but in any case is not such that all particles would be on top of each other and of course it does allow for an infinite universe.

Thanks phinds. Would you mind helping me to parse this response a little bit, to see if I can get a better understanding.

You're saying that the current model only allows us to extrapolate back to the end of the inflationary period. The statement above says that an inflationary state is past-timelike-incomplete, followed by the bolded statement, which you say is true given certain assumptions. Does this mean there are [at least] two options?

1. The bolded statement
2. An infinite universe

 

[Lynch101]

@phinds, you're talking about BB. The topic is specifically about inflation. I.e. that thing you tack on to the naive BB model at the early stages to (among other things) get rid of the singularity, also has a singularity. With the conclusion that maybe we need to duct tape something else at the early stages of inflation too.

Assuming the inflationary model is correct, does it say that inflation happened everywhere at the same time, and at the same rate?

Would the cause of inflation be the same everywhere?

 

[phinds]

You're saying that the current model only allows us to extrapolate back to the end of the inflationary period.

Yes.

The statement above says that an inflationary state is past-timelike-incomplete

That I don't know, but the inflationary period does not go back to the t0 that we get if we just extrapolate backwards from the current expansion ... it starts a staggeringly tiny amount of time after that.

Does this mean there are [at least] two options?

I don't like the bolded statement at all. Too many assumptions that seem unlikely. The infinite universe is a possibility. Since I don't think the bolded statement is true, I do NOT believe that the two options you listed are the only options.

I think you're trying to simplify something that cannot be definitively simplified in any known way (Nobel Prize territory).

The Big Bang Theory, the current model of cosmology, says that we understand how the universe expanded since the end of the (not definitively proven to exist) period of inflation. The period of inflation SEEMS to be likely since it's the best explanation we have for several things. Prior to the inflationary period there be dragons.

 

[Lynch101]

That I don't know, but the inflationary period does not go back to the t0 that we get if we just extrapolate backwards from the current expansion ... it starts a staggeringly tiny amount of time after that.

I don't like the bolded statement at all. Too many assumptions that seem unlikely. The infinite universe is a possibility. Since I don't think the bolded statement is true, I do NOT believe that the two options you listed are the only options.

Apologies, this will probably be a very naiive question, but how would extrapolating [further] backwards in time necessitate additional assumptions? Naiively, I would've thought that to justify not extrapolating further backwards, would require some additional assumption to justify why it wouldn't be possible.

By infinite universe do you mean an eternal universe which underwent inflation at some stage?

I think you're trying to simplify something that cannot be definitively simplified in any known way (Nobel Prize territory).

We might have to see if we can get someone to nominate us for this thread

I guess I am trying to simplify it for myself, as in simplify what the current position is.

The Big Bang Theory, the current model of cosmology, says that we understand how the universe expanded since the end of the (not definitively proven to exist) period of inflation. The period of inflation SEEMS to be likely since it's the best explanation we have for several things. Prior to the inflationary period there be dragons.

I was thinking that there might be some indication as to whether inflation had to be isotropic or not, such as galaxy formation or distribution of galaxies, or something.

 

[phinds]

... how would extrapolating [further] backwards in time necessitate additional assumptions?

What do you propose? That the universe just sprang into being at t0? Don't you think that's an assumption? Can you prove it? Can you prove that there was not some other mechanism happening prior to inflation? Can you prove ANYTHING about what was going on prior to inflation? No, you can't. That means that WHATEVER you believe was happening is an assumption.

 

[Lynch101]

What do you propose? That the universe just sprang into being at t0? Don't you think that's an assumption? Can you prove it? Can you prove that there was not some other mechanism happening prior to inflation? Can you prove ANYTHING about what was going on prior to inflation? No, you can't. That means that WHATEVER you believe was happening is an assumption.

I may be misinterpreting the statement I referenced in the OP and your subsequent response, but I don't see why it would require the universe springing into being at t0.

You seem to be saying that our current models only begin at t0+xt. I'm interpreting the emboldened statement above to say that if we extrapolate back to t0 then the particles will meet.

To me, it would seem that extrapolating back to t0 would not require any additional assumptions, whereas I would think that an additional reason would be required to justify not extrapolating back in time i.e. to say why we can't extrapolate back in time.

We could still have an eternal universe at t0.

 

[PeterDonis]

Firstly, it might be worth asking if anyone is familiar with the above paper entitled 'Inflationary spacetimes are not past-complete' by Arvind Borde, Alan H. Guth, Alexander Vilenkin?

We have had previous PF threads on this paper:

https://www.physicsforums.com/threads/what-is-the-borde-guth-vilenkin-theorem.934908/

https://www.physicsforums.com/threads/bgv-theorem-and-penroses-conformal-cyclic-cosmology.994703/

 

[Lynch101]

Just had a read of the other threads and I just want to check that I've correctly understood the key points.

...during inflation, any irregularities get smoothed out. Any matter that exists gets diluted so much that it effectively disappears.

That addresses my question about potential signatures of inflation having occurred non-uniformly, doesn't it?

If you take this fact and run the clock backward, it means that unless the inflating universe is perfectly empty, then the other matter exists during inflation will, looking into the past, get more dense. Eventually it will get dense enough that inflation is no longer possible. This indicates that inflation cannot be extended infinitely into the past. It had to have a beginning at some point.

Does this suggest that extrapolating inflation into the past would seem to suggest that a singularity would be inevitable, however, a singularity would be too dense to allow for inflation to occur?

There is some debate as to whether or not this theorem actually applies to our universe.

Is there a majority for either position in this debate?

 

[Bandersnatch]

That addresses my question about potential signatures of inflation having occurred non-uniformly, doesn't it?

Assuming the inflationary model is correct, does it say that inflation happened everywhere at the same time, and at the same rate?
Would the cause of inflation be the same everywhere?

Insofar as one's thinking about signatures of inflation in our patch of the universe, then they should be indeed smoothed - that's part of the raison d'etre of the model.
But when looking at the bigger picture, the inflationary universe is not uniform for most of its history. Patches of the inflating space constantly decay into regular expansion, while the remainder keeps inflating eternally into the future. The inflating regions always dominate over the regular patches, no matter how many nucleate.
The quoted paper argues that going back in time we see all the 'normal' universes roll back into the inflationary background, which, in finite time, reaches the moment when a singularity is inevitable.
At the moment just before the singularity, all of the inflating universe is uniform and whatever physics we were to tack on to jump-start it, it'd affect the entirety of it. In this sense, the cause would be universal.

 

[PeterDonis]

The quoted paper argues that going back in time we see all the 'normal' universes roll back into the inflationary background, which, in finite time, reaches the moment when a singularity is inevitable.

Note that there is an alternative scenario, in which the inflationary background, to the past of some instant of minimum scale factor, is contracting rather than expanding. This is what de Sitter spacetime looks like. The paper gives no argument that I can see for such an alternative scenario being impossible; its only real argument is that the authors don't like such a scenario because they think the universe should always be expanding. But not all physicists agree with that view; for example, proponents of models like the quantum "bounce" models would say that contraction to minimum scale factor followed by expansion is just the natural outcome of having a quantum field, such as the inflaton scalar field, that behaves like a cosmological constant, i.e., like de Sitter spacetime.

 

[elcaro]

Summary:: Is the below summation an accurate representation of the peer reviewed paper?

Firstly, it might be worth asking if anyone is familiar with the above paper entitled 'Inflationary spacetimes are not past-complete' by Arvind Borde, Alan H. Guth, Alexander Vilenkin? If you are, you might be able to help me with this question.

I was doing some reading trying to get a better understanding of 'the big bang' and a thread on here led me to an article on Forbes. I know pop-sci articles are not a good source of information but the article links to a peer reviewed paper* entitled 'Inflationary spacetimes are not past-complete'. I'm wondering if the emboldened comment from the author of the Forbes article is an accurate deduction from the paper.
Bold added by me.Forbes Article

If you are not familiar with the paper, is there perhaps additional information that I could provide that might be helpful? I'm not sure myself, but if there were something in particular you could suggest, I can take a look in the article.*At least I think it's peer reviewed.

This theorem in simple terms only proofs that an inflating spacetime must have had a start a finite time ago.
It does not imply anything else, and for instance it does not imply that time had a begin or that there must have been a singularity. None of that is implied.

If you combine this theorem with the fact that eternal inflation is generically future eternal, it can be shown that the finite amount of time that happened since eternal inflation started can be any amount of duration, without upper bound. We for instance don't know - and assuming that our universe was formed by eternal inflation - how long ago eternal inflation started, as it could be any amount of time. Presumably our universe was not formed directly or soon after inflation started as the probability of that would be infinitessimally low.

A further note is that generically eternal inflation starts a multiverse, as any part of the inflating space will decay after some finite time (creating a bubble universe), but due to the fact that the space that still inflates grows exponentially fast, inflation generically will last forever. But it is not considered that such an event (the start of eternal inflation) must have been a unique event. Considering that this pre-inflationary universe had a probability of starting eternal inflation in some part of its spacetime greater then zero, and assuming that spacetime would be spatially and temporally infinite, there presumably would have been multiple - unlimitly many - occasions of starting an eternally inflating branch. So in fact eternal inflation would lead to a multi multiverse.

This would imply that in some other part of space in the pre-inflationary spacetime, and even before our 'branch' of eternal inflation started, eternal inflation could have started, causing a separate branch of multiverse not connected to our spacetime. In most expositions of eternal inflation, this is not taken in consideration, as these other branches are not causally connected to our spacetime, as there is nothing that we can know about it, but the paradigma/theory of eternal inflation does not explicitly exclude it.

 

[PeterDonis]

Considering that this pre-inflationary universe had a probability of starting eternal inflation in some part of its spacetime greater then zero

The model under discussion is not probabilistic as far as the spacetime geometry is concerned. So there is no "probability" of eternal inflation starting at a given event or in a given region of the spacetime. There is simply an eternally inflating region, which is not past complete (so there might be another region, whcih would be a non-inflating region, before it), but whose boundary is fixed in the model, not probabilistic.

Given the above, I do not think your idea of a "multi multiverse" is applicable to this model.

 

[elcaro]

The model under discussion is not probabilistic as far as the spacetime geometry is concerned. So there is no "probability" of eternal inflation starting at a given event or in a given region of the spacetime. There is simply an eternally inflating region, which is not past complete (so there might be another region, whcih would be a non-inflating region, before it), but whose boundary is fixed in the model, not probabilistic.

Given the above, I do not think your idea of a "multi multiverse" is applicable to this model.

Indeed we do not know that. The conditions for which eternal inflation may or not may happen in the pre-inflationary spacetime vary over the model of inflation concerned. Some are probabalistic, which means, it might depend on quantum fluctuations. Chaotic eternal inflation (the theory of A. Linde - https://www.researchgate.net/publication/263979366_ETERNAL_CHAOTIC_INFLATION) already has probabalistic characteristics.

Citation from the above paper:

The eternal hilltop or chaotic inflation takes place when quantum fluctuations of the inflaton dominate over its classical motion. In the case of eternal hilltop inflation [22,23,54], it occurs in the vicinity of the local maximum of the potential where the classical motion vanishes, while in the case of eternal chaotic inflation [24][25][26], it occurs at large-field values for which the quantum fluctuation becomes significant. In either case, once the eternal inflation happens, it continues to inflate, which similarly helps to realize apparently fine-tuned parameters and/or initial conditions required for, e.g., the subsequent slow-roll inflation, curvaton scenarios, baryogenesis, etc.

 

[elcaro]

That I don't know, but the inflationary period does not go back to the t0 that we get if we just extrapolate backwards from the current expansion ... it starts a staggeringly tiny amount of time after that.

I don't think that your temporal ordering is quite right. First, what do you mean with T0, do you mean the initial singularity as proposed in models of the universe wihout inflation, where we only reason from the theory of GR? Such a model would predict indeed a T=0 in which everything would be stacked in a point, having infinite density and so on. This however is physical impossible, and we know therefore that GR is incomplete.

In the framework of inflation though, the hot big bang scenario (particle creation and particle/antiparticle annihilation leaving only a tiny amount of matter, expansion and cooling of the universe, and finally some 380.000 years later the universe cooled down enough to become transparent to light) starts AFTER inflation, not before.

Since chaotic eternal inflation is future eternal, and produces zillions of universe like ours, we do not know how long after the start of eternal inflation our universe formed. I don't think it likely that our universe formed right after the start of inflation, as it could have happened long periods of time after the start of inflation. It is quite imaginable that inflation already started zillions of years before our universe was born.