## Inflation (topic split)

Discussions ranging from space technology, near-earth and solar system missions, to efforts to understand the large-scale structure of the cosmos.

### Inflation (topic split)

BurtJordaan » September 2nd, 2017, 12:55 am wrote:
mitchellmckain » 01 Sep 2017, 21:45 wrote:So, what do you mean then when you say time is quantized but not space.

My understanding is that for quantizing of space to be consistent, we would need a consistent theory of quantum gravity. And AFAIK, we are not there yet. I think it is fairly well accepted that the Planck scale is where GR breaks down, but the Planck scale is not a "minimum scale" - things just get 'fuzzy' when we go smaller.

Ok, but how is time any different?

The point is that I am not aware of any proven formalism quantizing time apart from space. QFT which is based on relativistic QM, treats space-time as a 4 vector, so it is hard for me to see how such a distinction is even made. Note, this is not about the whole space-time thing, but trying to understand why you even had a reason to think in the first place that time was quantized but not space. Where did you get that idea from?

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### Re: Photon's puzzle.

I guess I got it from my cosmology studies, especially the inflation part of it (which is about as deep as I have gone into the quantum regime). There we regularly talk about time starting at one Planck time, with space infinite, but with quantum field fluctuations below the Planck scale. Now this may not equate to time being quantized, but that's anyway how I have always pictured it - perhaps wrongly.

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### Re: Photon's puzzle.

This is now way off topic, but for me Occam's razor says that Inflation have most likely delivered a perfectly flat expanding space (not flat spacetime of course, since it is expanding). Another cut by Occam then prefers an infinite thing to start with and energy density at the Planck scale everywhere (the singularity).

More connected to the topic, some of the light, or photons if we like, that escaped the 'last scattering event' reached us presently as the CMB and they are still coming from all directions, just from farther and farther regions. We do see them affected by the matter along their path, so I think this also answers @bangstrom's query about how we know that light propagates from source to receiver.

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### Re: Photon's puzzle.

BurtJordaan » September 3rd, 2017, 1:56 am wrote:This is now way off topic, but for me Occam's razor says that Inflation have most likely delivered a perfectly flat expanding space (not flat spacetime of course, since it is expanding). Another cut by Occam then prefers an infinite thing to start with and energy density at the Planck scale everywhere (the singularity).

If the universe was infinite to start then there is no way that inflation explains that the universe is uniform everywhere, but only uniform in this portion of the universe. The whole idea of inflation was that the universe we see originated in a very close area, but if the universe was infinite then that obviously does not apply. Thus it is only if the universe is finite that inflation gives us an explanation for why the universe is uniform everywhere. So an infinite universe leads to supposing an extra portion of the universe which we cannot know anything about, even that it is anything like what we can see.

To use Ocaam's razor to as you have done is purely subjective support for a personal preference for the universe to be infinite. Like I explained here Occam's razor really only has substance when we are talking about unfalsifiable elements added to the theory, otherwise correct science is a matter of accuracy not simplicity. Besides, there is no added complexity to a finite universe whatsoever. The theory works just fine for both finite and infinite universe. But with the finite universe we don't have to suppose an unknowable unfalsifiable infinite extension of the observed universe.

BurtJordaan » September 3rd, 2017, 1:56 am wrote:More connected to the topic, some of the light, or photons if we like, that escaped the 'last scattering event' reached us presently as the CMB and they are still coming from all directions, just from farther and farther regions. We do see them affected by the matter along their path, so I think this also answers @bangstrom's query about how we know that light propagates from source to receiver.

Except, it should be noted that an open universe, as we now believe is the case, means that expansion is accelerating and thus the portion of the universe we can eventually see (i.e. the portion within the event horizon) is actually shrinking. It may be farther and farther but only because of expansion, when the fact is that we are actually seeing less and less.

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### Re: Inflation (topic split)

(The only one I see missing is the one that should be third in the thread) I found it in another thread with the same title as the original "photon's puzzle". I post it here...

[[Mod note: Thanks. I have deleted the 'orphaned' post in Physics. This one sits slightly out of chronology, which i do not know how to fix. Will ask one of the Admins.]]

Ahh yes...

I, for example, typically have the image in my head of the universe being spatially finite and have to remind myself that we don't actually know whether it is finite or infinite, since the theory (GR) works either way. But when I picture it in my head, most of the time I picture the big bang starting with an infinitesimally small space and expanding to a large but finite size. I suppose I find that easier to believe.

This might even be a case where I would be tempted to employ the Occam's razor argument. The infinite universe would have us suppose that there is larger universe beyond our ability to ever detect it. Most may greatly different than our own since the whole inflation argument simply explains why the detectable universe is so uniform but if the universe was infinite in the beginning then the whole thing need not be uniform. But it is the unknowability of this "rest of the universe" that bothers me almost as much as the usual scientist aversion to infinities. Thus this seems both an unnecessary add-on as well as likely unfalsifiable and would thus I would gravitate to the rather simpler idea of a finite universe, which fits more naturally in my mind with a universe which has a finite past.

I guess we leave the question open to the possibility of a theoretical determination since an experimental determination is out of reach. It is certainly in the spirit of scientific inquiry to keep to the honest fact that we do not know, and having been burned by the failure of previous assumptions of a steady-state universe, it is understandable that we would want to avoid making a similar mistake.

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### Re: Inflation (topic split)

If everything is infinitely divisible, then I'd suppose that not anything ever needs to bang, due to an infinite density absorbing everything; however, if the lowest size thing has a finite limit, then I could understand some conglomeration accumulating having to bang when there is no 'inward' left for it to compress into. This depends on if fields are things with substance,I guess.

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### Re: Inflation

mitchellmckain » 03 Sep 2017, 10:25 wrote: Thus it is only if the universe is finite that inflation gives us an explanation for why the universe is uniform everywhere. So an infinite universe leads to supposing an extra portion of the universe which we cannot know anything about, even that it is anything like what we can see.

All mainstream inflation versions indicate that our observable universe was always just a small portion of the whole. In fact, since they predict a spatially flat total universe, there is no simple way not to make it infinite. And we do observe the spatial flatness in the CMB (our 'local patch'), with just the right amount of inhomogeneity and other characteristics.[a]

IMO, this is a case where Occam should not cut off the unobservable parts, because we have no theory for how it could not be there and not be just be more of the same. It is not unfalsifiable elements added - it has to be there right from the bang (which happened everywhere, singular in time, but not in space). Otherwise the theory must be wrong, but everything that we have observed so far seem to fit the theory.

The problem seems to be that we have many versions of inflation that predict the same, presently observable and unobservable outcomes, but with different mechanisms or beginnings. And we do not have the technology to test for the tiny differences that might be observable. So near the beginning, they might all be wrong. ;)

-0-

[a] Standard inflation postulates exponential expansion, which starts with a long period of slow expansion, i.e. something like scale factor evolution of $\large a = be^{k t}$ with $b$ the scaling constant and $k$ the time constant.

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### Re: Inflation

BurtJordaan » September 4th, 2017, 1:14 am wrote:All mainstream inflation versions indicate that our observable universe was always just a small portion of the whole.

That much is correct.

BurtJordaan » September 4th, 2017, 1:14 am wrote: In fact, since they predict a spatially flat total universe, there is no simple way not to make it infinite. And we do observe the spatial flatness in the CMB (our 'local patch'), with just the right amount of inhomogeneity and other characteristics.[a]

IMO, this is a case where Occam should not cut off the unobservable parts, because we have no theory for how it could not be there and not be just be more of the same. It is not unfalsifiable elements added - it has to be there right from the bang (which happened everywhere, singular in time, but not in space). Otherwise the theory must be wrong, but everything that we have observed so far seem to fit the theory.

Where are you getting this? Because it just isn't true. Cosmology has never answered the question of whether the universe is finite or infinite because big bang theory works fine in either case.

Inflation theory was devised to explain why the universe we can see is uniform on a large scale, by having it all originate in a small area in the early universe. But if the universe is infinite then it started out as infinite and all of it did not originate from a small area. Thus inflation would only predict uniformity in what we observe and not in the rest of the universe.

The only place I see a connection is in the inflationary theories called eternal inflation. But these have certainly not been established as fact. Nor do I see the claim that eternal inflation requires an infinite universe, only that it produces an infinite number of universes in a multiverse. But still, no matter how much you might agree with Linde and Guth who favor eternal inflation leading to an infinite multiverse, this is very much a soft area of cosmology where there is no consensus and the biggest objection is that it simply isn't testable. In my book that makes it more a matter of subjective personal philosophy rather than objective science.

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### Re: Inflation

mitchellmckain » 04 Sep 2017, 09:33 wrote:
BurtJordaan » September 4th, 2017, 1:14 am wrote:IMO, this is a case where Occam should not cut off the unobservable parts, because we have no theory for how it could not be there and not be just be more of the same. It is not unfalsifiable elements added - it has to be there right from the bang (which happened everywhere, singular in time, but not in space). Otherwise the theory must be wrong, but everything that we have observed so far seem to fit the theory.

Where are you getting this? Because it just isn't true. Cosmology has never answered the question of whether the universe is finite or infinite because big bang theory works fine in either case.

Cosmology observationally found our patch to be spatially flat to within 1 part in a 1000,[a] without being able to say on which side of flatness it is. This translates (cosmologically) back to after-inflation spatial flatness of less than 1 part in more than 1060. Such flatness translates for all practical purposes to 'infinite' in size and is why modern cosmology says: "our best buy is that it started out infinitely large".

Although this flatness is essentially what inflation also predicted (and also unable to predict on which side of zero spatial curvature it ends up), I must say cosmologists usually talk of "after-inflation" as the "start time" for their models.

Inflation theory was devised to explain why the universe we can see is uniform on a large scale, by having it all originate in a small area in the early universe.

This may have been the idea in the 1980s and 90s, but all modern versions are based on the 'slow roll inflaton field' which (AFAIK) is not bound to a small location in any background space. Yes, our observable universe must have been, but then we should not be talking about "the universe".

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### Re: Inflation

BurtJordaan » September 4th, 2017, 9:58 am wrote:Cosmology observationally found our patch to be spatially flat to within 1 part in a 1000,[a] without being able to say on which side of flatness it is. This translates (cosmologically) back to after-inflation spatial flatness of less than 1 part in more than 1060. Such flatness translates for all practical purposes to 'infinite' in size and is why modern cosmology says: "our best buy is that it started out infinitely large".

Although this flatness is essentially what inflation also predicted (and also unable to predict on which side of zero spatial curvature it ends up), I must say cosmologists usually talk of "after-inflation" as the "start time" for their models.

The possibilities are these.
Closed: Positive space-time Curvature. The universe expands at a decelerating rate until it starts collapsing again. Space-time is finite at least in the time dimension.
Open: Negative space-time Curvature. The universe expands hyperbolically approaching a non-zero expansion rate. Space-time is infinite because it never stops expanding.
Flat: Zero space-time Curvature. The universe expands asymptotically approaching a zero expansion rate. Space-time is infinite because it never stops expanding.

But none of these determine whether space by itself is infinite or finite. This is an unanswered question. Could you be confusing infinite space-time with infinite space? These are two different things.

Judgement on which of these is the case has been going back forth for decades. It is certainly close to zero curvature. For a while evidence suggested that it was open and the most recent evidence suggests it is flat.

BurtJordaan » September 4th, 2017, 9:58 am wrote:
Inflation theory was devised to explain why the universe we can see is uniform on a large scale, by having it all originate in a small area in the early universe.

This may have been the idea in the 1980s and 90s, but all modern versions are based on the 'slow roll inflaton field' which (AFAIK) is not bound to a small location in any background space. Yes, our observable universe must have been, but then we should not be talking about "the universe".

What is your source for this, please? The scientific papers I have read about slow role inflation since you mentioned it don't say any such thing - quite the opposite. I frankly don't see how this solution to the reheating problem can change the basic idea of inflation to such a great degree.

But in any case, just because a theory is newer doesn't make it correct. Fact in science is still established by objective evidence and not just by what is fashionable. Even evidence for inflation is still in dispute. Without evidence to back up theory, it is all nothing more than speculation. I am all for taking scientific discovery seriously and thus do not support Kuhn's scientific revolutions and other rhetoric for dismissing scientific findings. But there is still a difference between what is founded on evidence and what is just speculation. Furthermore, there is another problem with basing answers to questions like we are discussing on new theory. All the implications and details of the theory haven't been fully explored yet, so it is rather premature to jump to conclusions. The string of "ifs" in this kind of speculation get so long it is more than a little tenuous.

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### Re: Inflation

mitchellmckain » 04 Sep 2017, 19:45 wrote:But none of these determine whether space by itself is infinite or finite.

I think we are talking past each other here. I was only referring to spatial curvature, not spacetime curvature, which we today know is permanently negative due to the accelerated expansion.

As you surely know, spatial curvature depends on the energy content v.s. expansion rate and is today observed to be so close to zero that we cannot determine on which side of 'flat' it sits. The CMB indirectly gives us these 'triangles' to measure up for spatial flatness and this is what we get with very small uncertainties.

All the usual forms of inflation models 'deliver' an essentially perfectly flat space to the LCDM model, which is then already essentially infinite. Hence the claim that the universe (without multiverse assumptions) must be essentially infinite, otherwise 'new physics' is needed. Yes, because of the limited time since inflation, the particle horizon and the Hubble radius are finite, because they belong to our patch. This much is reasonably certain.

I agree that the origin of inflation is uncertain and that claims for that regime is speculative, but inflation against the (infinite) quasi-de Sitter spacetime background is particularly interesting to me. Sean Carroll and Jennifer Chen described this (and other models) well in Spontaneous Inflation and the Origin of the Arrow of Time.

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### Re: Inflation (topic split)

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### Re: Inflation (topic split)

Cool! This diagram illustrates a spatially flat universe with curved de Sitter spacetime very nicely.

As I understand it, from bottom to top, our entropy-driven observable universe started out as a very large (finite) patch on an infinite flat background spacetime. Because static de Sitter spacetime is unstable and will either collapse or expand, "our patch" collapsed to very a tiny volume and then must have undergone some form of inflation with particle creation, in order to create our presently observable universe.

I think present mainstream cosmology largely ignores the collapsing part, because there is very little chance that observations can ever confirm it.

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### Re: Inflation (topic split)

BurtJordaan ,

I'd like to think they are different, but my mind can't honestly deny the analogies. There is a much older theory given by Stephen Hawking that has this collapse and re-expansion dynamic.

He asks the reader to imagine a globe with a circular chain laying on it. (Take off a necklace and place it on a globe or ball in your house). If you roll a chain on a spherical surface, and that chain is connected, the result is that the chain's wide circle will shrink in diameter. Eventually, after much "rolling" the chain will shrink into a dot on one of the poles of the globe. If you continue rolling in the same direction, the chain will collapse to a singular point, but then start growing again. It is not a "bounce". It is the circle passing through itself without any discrete, (or discontinuous) disruption in the smooth rolling process. Continue rolling the chain after this. It will again chase itself to the opposite side of the globe, shrink to a point, and then grow again in the other direction. Speed up the "video" to 4X. This process will continue indefinitely, growing and shrinking, back and forth, from pole to pole.

Now lets explore the analogies between Hawking's and Carroll's cosmologies. Notice that after the chain shrinks to a dot, it then re-expands in the "opposite direction" on the globe. Notice that Carroll says observers in both the backward moving and forward-moving universes will claim that each of the other is in each other's "past". In either direction from the "static desitter vacuum" the arrow of time is pointing in opposite directions. Even though the dynamic of Hawking's Chain (lets call it) has no formal change in direction (discontinuous inexplicable reversal) , observers in both outgoing universes will have time progressing in opposite directions.

So yeah. I consider these theories, and I honestly get the impression they are the same theory, expressed in two different ways.

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