How long did inflation last in an eternal inflating universe?

[elcaro]

TL;DR

The model of eternal cosmological inflation states that once inflation begins, it generically never ends. But in any patch of space within this eternal inflating universe, inflation always effecively ends after a finite amount of time. From cosmological data we can only deduce a minimum amount of time (or e-foldings) must have happened before our universe was formed, but is there any data or anything within the theory that can tell us anything about how long inflation has lasted?

In so far I know eternal inflation can only constraint the minimum duration that inflation happened to produce the properties of the universe we can experimentally test (a minimum of some 60 e-folds, or in time, at least some 10^-30 seconds), but as eternal inflation is generically eternal to the future, is there some upper bound to the duration of the inflationary process, is there any theoretical or experimental data that can constraint the upper bound, or is that duration unbounded (can grow to infinity)?

 

[phinds]

How long is a line from zero to minus infinity?

 

[elcaro]

How long is a line from zero to minus infinity?

It has the same size as a line from zero to plus infinity.

But how does that answer my question?

Eternal inflation is not past eternal, so I don't see how that answers my question.

 

[phinds]

Eternal inflation is not past eternal, so I don't see how that answers my question.

I was under the impression that is IS past eternal. If it's not, then you are correct that my question is not relevant.

 

[elcaro]

Maybe my question was not clear enough, I am of course not asking how long (in general) eternal inflation lasts, cause that is infinite time, since it never stops generically. I am however asking how long ago (since now, or since inflation effectively stopped in this part of the universe) inflation has started, of which we only know its minimum value (namely some 10^-30 seconds) but not its maximum value. As eternal inflation is not past eternal, what are the bounds then for how long ago inflation must have started?

 

[elcaro]

I was under the impression that is IS past eternal. If it's not, then you are correct that my question is not relevant.

There is this theorem by Guth and Vilenkin, which states that eternal inflation has no geodesical complete past, which effectively means you can not extend it to the infinite past. So, a finite time ago, inflation must have started. But what is the upper bound for the amount of time that has elapsed since inflation started? My assumption is there, since I can't find any mention in the theory of an upper bound, nor a limit imposed by experimental data, that this duration is unbounded. So, inflation could have lasted 10^-30 seconds before it ended in this part of space, or it could have lasted a googleplex years or whatever large number one can come up with.

 

[phinds]

Maybe my question was not clear enough

I believe your question was clear, I just went with something I read some time back, and possibly misunderstood, that left me with the impression that eternal inflation WAS infinite in the past.

 

[PeterDonis]

I was under the impression that is IS past eternal.

No, it isn't. We have a recent thread on the paper by Borde, Guth, and Vilenkin that demonstrated this result:

https://www.physicsforums.com/threa...ary-spacetimes-are-not-past-complete.1004735/

 

[elcaro]

No, it isn't. We have a recent thread on the paper by Borde, Guth, and Vilenkin that demonstrated this result:

https://www.physicsforums.com/threa...ary-spacetimes-are-not-past-complete.1004735/

Does this theorem imply some kind of upper boundary for the maximum duration inflation could have lasted?

Are for instance longer durations for example increasingly less likely, and short durations more probable?

 

[PeterDonis]

Does this theorem imply some kind of upper boundary for the maximum duration inflation could have lasted?

I don't think so. It just says an inflating spacetime must be past incomplete; it doesn't give any kind of probability distribution that I can see for different possible finite durations of inflation into the past.

 

[kimbyd]

I don't think so. It just says an inflating spacetime must be past incomplete; it doesn't give any kind of probability distribution that I can see for different possible finite durations of inflation into the past.

Yeah. There's no known way to consistently describe probability in an eternal inflation scenario.

 

[elcaro]

Yeah. There's no known way to consistently describe probability in an eternal inflation scenario.

If it deals with infinities, that would be true, but since inflation is not past eternal, the volume of inflating space and the number of universes therein, can grow incredible large, yet never reaches infinity. So, in theory, it could be dealt with i would assume...

 

[kimbyd]

If it deals with infinities, that would be true, but since inflation is not past eternal, the volume of inflating space and the number of universes therein, can grow incredible large, yet never reaches infinity. So, in theory, it could be dealt with i would assume...

I suspect the problem is that eternal inflation is always infinite because it is future-eternal.

 

[PeterDonis]

since inflation is not past eternal, the volume of inflating space and the number of universes therein, can grow incredible large, yet never reaches infinity.

In the simplest eternal inflation model, both the inflating space and every "bubble universe" born from it are spatially infinite.

I don't know if there are inflation models in which the inflating space is spatially finite.

 

[elcaro]

In the simplest eternal inflation model, both the inflating space and every "bubble universe" born from it are spatially infinite.

I don't know if there are inflation models in which the inflating space is spatially finite.

You may be right on that. Don't know if the number of universes is also assumed to be infinite.

My naive assumption though was that inflation can start from a small volume of space, and grows exponentially, and thus would never be infinite, but would grow without bounds into the eternal future. "Bubble universes" are a bit weird in that they can be fnite from outside, yet infinite from inside. Also I would assume the "start of inflation" would not be a unique event, but would also go on in different part of spacetime. There is however nothing in the theory of eternal inflation that makes any assumption about the pre-existing spacetime before inflation, and wether inflation can or can not start multiple times. It would be quite hard to make any assumptions about this, because almost nothing can be known about the pre-existing universe before inflation starts, except for the conditions under which inflation can start, depending on the exact inflation model.

 

[PeterDonis]

inflation can start from a small volume of space

Not in the simplest eternal inflation model I described; in that model, the "volume of space" is always infinite, and inflation does not increase the "volume of space".

 

[kimbyd]

In the simplest eternal inflation model, both the inflating space and every "bubble universe" born from it are spatially infinite.

I don't know if there are inflation models in which the inflating space is spatially finite.

Here's one example:
https://arxiv.org/abs/1410.6065

It's not eternal inflation, but it's a way to describe inflation in explicitly finite terms.

 

[elcaro]

Not in the simplest eternal inflation model I described; in that model, the "volume of space" is always infinite, and inflation does not increase the "volume of space".

In that case I do not quite understand why eternal inflation can not be past eternal...

 

[PeterDonis]

In that case I do not quite understand why eternal inflation can not be past eternal...

Because "volume of space" is not the right criterion to use. The right criterion to use is the expansion of an appropriate congruence of timelike or null worldlines. If that expansion is everywhere positive in some region of spacetime, it is impossible for that region of spacetime to extend infinitely far into the past. That is the basic conclusion of the BGV theorem.

 

[elcaro]

About the duration of inflation, in this paper (Inflationary Paradigm after Planck 2013) on page 4 (right column second paragraph) it is stated:

If this multiverse picture is combined with rather mild assumptions about anthropic selection effects, then it becomes very plausible that we live in a pocket universe which has undergone inflation, with no particular prejudice about whether the potential is plateau-like or not. As described above, the pocket universe after tunneling would be a homogeneous open universe, with the scalar field that tunneled starting with φ˙ = 0. The amount of slow-roll inflation that follows depends on the shape of the potential. Statistics alone would presumably favor small amounts of inflation if any, but Refs. [33] and [39] argue that simple assumptions about the probability distribution for slow-roll potentials imply that the probability density for having N e-folds of slow-roll inflation falls off for large N only as a power of N: P(N) ∼ 1/N^p , with p ≥ 0 and p ∼ O(1). Furthermore, Ref. [33] argues there there is an anthropic minimum for the duration of the slow-roll inflation, N >∼ 59.5, based on the requirement that galaxy formation is possible. We consider this a rather mild anthropic assumption, motivated by logic that parallels closely the logic of the anthropic bound on vacuum energy density [21]—both vacuum energy and curvature suppress the growth of structure.

If I interpret this correctly the amount of inflation, its duration, or the number of e-folds N, falls off for large N as 1/N^p (p >= 0), so longer duration is less likely.

 

[kimbyd]

In that case I do not quite understand why eternal inflation can not be past eternal...

It requires infinite fine-tuning.

Inflation has the effect of making the universe smoother over time. But the laws of physics are valid in reverse as well as forward. So if you run the clock the other way, any tiny deviation from flatness will grow until it causes a singularity in the finite past.

 

[256bits]

It requires infinite fine-tuning.

Inflation has the effect of making the universe smoother over time. But the laws of physics are valid in reverse as well as forward. So if you run the clock the other way, any tiny deviation from flatness will grow until it causes a singularity in the finite past.

with the mutliverse, and island pockets of universes, with the laws of physics possibly, or probably, different in each one, doesn't the initial inflation have to include all of these physical laws, so that each pocket universe could be a subset of the - I'll refer it to as the - grand physical law.

 

[kimbyd]

with the mutliverse, and island pockets of universes, with the laws of physics possibly, or probably, different in each one, doesn't the initial inflation have to include all of these physical laws, so that each pocket universe could be a subset of the - I'll refer it to as the - grand physical law.

The way this is generally attacked in theoretical physics is via symmetry breaking. You have a fundamental law which obeys some complicated symmetry like SO(10). That gets broken into the less symmetric standard model through some process (SU(3) X SU(2) X U(1)).

That symmetry breaking can happen in a great many ways, depending upon the theory. It could break down into the same symmetry groups but with different parameters, for example. Or it could break down to completely different symmetry groups altogether.

In string theory, for instance, the symmetry breaking comes from compactification: string theory predicts a bunch of extra dimensions that have to be small to fit observations. The number of ways in which they can be made small is extremely large, which leads to different types of symmetries with different parameters.

 

[elcaro]

It requires infinite fine-tuning.

Inflation has the effect of making the universe smoother over time. But the laws of physics are valid in reverse as well as forward. So if you run the clock the other way, any tiny deviation from flatness will grow until it causes a singularity in the finite past.

The laws of nature are time symetric, yet we do have an axis of time due to entropy. We can distinghuish between a glass falling to the ground and smashing to pieces as the forward direction of time, and pieces of glass assembling themselves into a glas, and moving upward as the backward direction of time. Why would this have been different in the early epoch of the universe during inflation? The only or major difference is that there were no particles yet with mass, so without mass, no arrow of time?

Since inflation can start from a very small patch of space, and inflation can be generically future eternal, why couldn't we assume the starting patch of space was already smooth to begin with?

 

[elcaro]

It requires infinite fine-tuning.

Inflation has the effect of making the universe smoother over time. But the laws of physics are valid in reverse as well as forward. So if you run the clock the other way, any tiny deviation from flatness will grow until it causes a singularity in the finite past.

Inflation does not only smooth the universe, it also creates small inhomogeneities due to quantum fluctuations, which leads to one of the observable features inflation may have left in the CMB spectrum. Don't these features break time symmetry?

 

[elcaro]

No, it isn't. We have a recent thread on the paper by Borde, Guth, and Vilenkin that demonstrated this result:

https://www.physicsforums.com/threa...ary-spacetimes-are-not-past-complete.1004735/

Some note on this, in the follow up of this theorem, there are two distinct proposals worth mentioning, the first one is the idea that maybe one should consider the possibility that the universe sprang "out of nothing" so to speak (buble nucleation - Coleman-DeLuccia tunneling - from a small spacetime with a radius which you then shrink to 0 size to approximate a "physlcal nothing") - the position that Vilenkin and others take on this, and the proposal (Sean Carol, Guth) that our universal timeline is supplemented with a "negative" timeline (time flowing backwards), in which case the universe IS past eternal.

And as an add-on question, I wondered wether there aren't more possibilities where the universe is past-eternal without the need of a past time line in which time flows backwards, for example by assuming that the pre-existing space time before inflation started that produced our universe, there were also different branches of inflation happening (as inflation only needs to start in a small patch of space) in that pre-existing spacetime in different parts of that spacetime and even before the inflationary process that produced our universe had begun.

 

[thegroundhog]

Having read this thread, I'm still unclear regarding use of the word infinite. I have been reading Max Tegmark who mentions Eternal Inflation as being infinite, but if it had a finite past this can't be possible. Also, what does spatially infinite mean? If space is growing from a point then it can't be infinite, surely? In my simple view you can only talk about something being infinite if it started that way.

And as an add-on question, I wondered wether there aren't more possibilities where the universe is past-eternal without the need of a past time line in which time flows backwards, for example by assuming that the pre-existing space time before inflation started that produced our universe, there were also different branches of inflation happening (as inflation only needs to start in a small patch of space) in that pre-existing spacetime in different parts of that spacetime and even before the inflationary process that produced our universe had begun.

If, at some point time was going backwards, presumably with respect to how we see it, as there is no absolute arrow of time, and it's infinite, doesn't that create a paradox whereby how does something change or start if there is an infinite amount of time preceding it?

 

[valenumr]

I suspect the problem is that eternal inflation is always infinite because it is future-eternal.

Is eternal inflation compatible with the observable universe?

 

[PeterDonis]

I have been reading Max Tegmark who mentions Eternal Inflation as being infinite, but if it had a finite past this can't be possible.

Sure it can. By "infinite" Tegmark means infinite into the future. Eternal inflation does have that property.

If space is growing from a point

It isn't. That is not how the expansion of the universe works.

If, at some point time was going backwards

There are models that have a region in the past with this property (such as the model proposed by Carroll and others--I can't find a reference right now but I think we have had past PF threads about it), but these are different from the eternal inflation models being discussed in this thread so they are off topic for this thread.

 

[PeterDonis]

Is eternal inflation compatible with the observable universe?

Yes. Why wouldn't it be?