Where' the hoops? 145 e-fold inflation predicted

[marcus]

There's a belief floating around that it takes "jumping through a lot of hoops" for a theoretical model to predict inflation AND give an adequate amount AND then stop . The conventional wisdom is it requires fine-tuning for inflation to turn on, go for at least 60 efolds, and then turn off, i.e. make a 'graceful exit'.

This unnaturalness ailment afflicts models where the bout of inflation is triggered by a random fluctuation in a quantum field. It does not afflict LQC models where inflation is triggered by a bounce.

So the conventional wisdom seems reasonable enough if you steadfastly ignore bounce cosmology models. But it's getting harder to do that---it takes determination, these days, not to pay attention.

Barrau has been invited to give one of the plenary talks at Loops 2013 next month at Perimeter.

http://arxiv.org/abs/1301.1264
Duration of inflation and conditions at the bounce as a prediction of effective isotropic loop quantum cosmology
Linda Linsefors, Aurelien Barrau
(Revised 3 Jun 2013 (this version, v2))
Loop quantum cosmology with a scalar field is known to be closely linked with an inflationary phase. In this article, we study probabilistic predictions for the duration of slow-roll inflation, by assuming a minimalist massive scalar field as the main content of the universe. The phase of the field in its "prebounce" oscillatory state is taken as a natural random parameter. We find that the probability for a given number of inflationary e-folds is quite sharply peaked around 145, which is consistent with the most favored minimum values. In this precise sense, a satisfactory inflation is therefore a clear prediction of loop gravity. In addition, we derive an original and stringent upper limit on the Barbero-Immirzi parameter. The general picture of inflation, superinflation, deflation, and superdeflation is also much clarified in the framework of bouncing cosmologies.
7 pages, 7 figures

 

[Haelfix]

Quantum cosmology is about an order of magnitude more speculative than anything to do with inflation, which hinges on well understood semiclassical analysis. Loop quantum cosmology in particular relies on extremely shaky theoretical underpinnings that are not understood at this time and is an active research area.

Worse, it actually relies on an adhoc semi classical inflaton field put in by hand at the end in order to have any hope of reasonable physics. In this sense, it's much more similar to multi field models where you have several bouts of inflation, and the slow roll assumptions can be dropped.

In fact the multiverse problem is just as much of an issue in this class of models as in any normal inflationary scenario. The problem again is one of principle. The enormous amount of exponential, exponential acceleration that these models predict make the problem worse, not better as it implies enormously larger volumes of space and much longer timeframes. Recall that any physics described by an ergodic Hamiltonian system returns arbitrarily close to any point in its phase space. In particular, if the conditions that are necessary and sufficient for a bounce to occur are generic like Ashtekar claims, then the miracle is explaining why this only happens once. You see the dilemma.. Either you have a very unnatural and rare event at a very special point in space and in time given by a small volume in phase space, or you have a generic physical mechanism that occupies a large volume in phase space. The anthropic principle is required for the former, the latter really implies a multiverse unless you happen to be at a very unusual moment in time.

Yet another way to see the problem, is to understand that you will have regions of inhomogeneities generically when considering such large spatial volumes and the more relevant classical equations of motion that need to be solved for is not the FRW class of metrics, but rather something more like the Swiss cheese models. Anyway Bojowald has written about such matters here:
http://arxiv.org/abs/1212.5150

 

[marcus]

Perhaps we should try to understand the model a bit, before rendering opinions about it. It is based on two equations: one being the familiar Friedman equation and the other a scalar field. The form of the quantum corrected Friedman equation is standard in LQC. As one easily sees, the correction term is suppressed except at at extreme density when rho approaches the critical level at which rebound occurs.
H² = κ/3 ρ(1 - ρ/ρ_c)
The other equation is that of a scalar field with mass m:
φ'' + 3Hφ' + mφ = 0

These are equations (1) and (2) of the paper and in effect completely describe the model. The two equations are remarkably simple and have only two adjustable parameters. The results are not sensitive to varying the parameters but benchmark settings were used for definiteness in the presentation. Their benchmark scalar field mass was taken over from Andrei Linde (known for his work on inflation) and their benchmark critical density is what was found by Ashtekar et al around 2007 and used consistently in LQC since then. In their numerical work they also let both the mass m and the critical density vary and report the results.

 

[Haelfix]

Perhaps we should try to understand the model a bit, before rendering opinions about it.

I agree but you should take your own advice and actually understand the work before ascribing claims to the paper that it does not support. What you have in the linked paper amongst other things is the equation for a scalar field, with a canonical kinetic term and a quadratic potential. This is all quite standard slowroll inflation, and so contrary to claims you made in the other thread, this does mean you have the picture of a field rolling down a potential in the usual sense of not slipping. What LQC does for you is to generate early initial conditions from the bounce as well as to calculate the central value of some PDF that will fix several of the constant values appearing in the inflation phase conditions, and these determine a few extra undetermined free parameters in the dynamics. So for instance, this determines how many efolds you expect inflation to undergo.

Its worth emphasising that this is far from a realistic scenario. Amongst other things the particular choice of inflaton considered is ruled out by the Planck satellite results, there is something a little strange going on with the inverse reheating equations but most importantly there is far too much symmetry in the problem. This is typical of LQC papers, where they keep as much homogeniety and isotropy as possible for calculational traction. Of course, this is exactly what good researchers do to simplify a problem, and to gain intuition for what happens in the general case. Of course the flipside is that in the non symmetry reduced problem, during the FRW evolution phase of the universe you will generate causally disconnected horizons in the usual way, and when you consider the recollapse phase, you will run into the exact same issues that Bojowald was talking about in the linked paper and the multiverse comes right back into the picture.

More to the point, the above paper does not contradict anything that I wrote above. If the generation of generic initial conditions proceeds as explained in the paper, you have a real problem explaining why this doesn't happen in some other part of space as well. And you are right back into the usual choice between extreme finetuning and horizon problem temperature conspiracies, or occupying some some highly nonCopernican place in the universe or having a multiverse whether you like it or not.

 

[marcus]

What you have in the linked paper amongst other things is the equation for a scalar field, with a canonical kinetic term and a quadratic potential. This is all quite standard slowroll inflation,...

Exactly! This is one of the things I like about their paper. It is obviously a simple quadratic potential, not (as I said) a funny-shaped plateau potential. We've probably all seen contrived inflaton potentials described picturesquely in terms of hats and the like.

The key thing is their bout of inflation is driven by a bounce. The collapse of a prior phase of the universe.
It does not require a "quantum fluctuation" that puts the scalar field on a "false vacuum" plateau, in order to get started.

I'm not sure how you get from there to a "multiverse", but maybe I don't understand what you mean by that term. Does the idea of a collapsing phase---in our causal past---constitute a "multiverse" for you? I didn't introduce the "multi" topic in this thread because for one thing it is darned vague, people imagine it meaning many different things. But since you brought it up perhaps you could explain why Barrau Linsefors' type of bounce-trigger inflation should lead to what you think of as a "multiverse".

 

[marcus]

..., if the conditions that are necessary and sufficient for a bounce to occur are generic like Ashtekar claims, then the miracle is explaining why this only happens once. ...[/url]

I'm curious to know where you saw Ashtekar claim this, and to find out what he could have meant by it. IIRC in models from Ashtekar's et al the bounce is caused by the collapse of a whole classical universe. Other authors have discussed the possibility that a black hole collapse could initiate expansion of the sort we live in, but I don't think Ashtekar has ever subscribed to that.

By "generic" do you mean "generic every time an entire classical universe collapses"?

 

[Haelfix]

I'm curious to know where you saw Ashtekar claim this, and to find out what he could have meant by it. IIRC in models from Ashtekar's et al the bounce is caused by the collapse of a whole classical universe. Other authors have discussed the possibility that a black hole collapse could initiate expansion of the sort we live in, but I don't think Ashtekar has ever subscribed to that.

By "generic" do you mean "generic every time an entire classical universe collapses"?

I mean that the conditions for inflation are claimed to occur with high probability in a region of space after a specific set of conditions are met (after the bounce expansion phase).
http://arxiv.org/abs/1103.2475.

At this point, all you need is a sufficiently large volume of space and long enough time frames, and if you believe in unitarity physics, the same conditions *must* occur somewhere else. At the end of the day, its just a principle of quantum mechanics. Something that is not forbidden, will eventually occur, and occur infinitely many times given infinite time frames.

Now, its easy to see that the actual dynamics will look like the scenario that Bojowald describes. After the FRW evolution stage of the LQC picture, b/c of the enormous total spaces involved, two distant patches of the sky will eventually fall so far out of causal contact, that it no longer makes sense to describe the universe exactly as a FRW solution. Past a certain distance scale, and given enough time we know that the assumptions of Homogeneity and isotropy cannot hold exactly. We don't know exactly how to precisely model this with GR, but you typically see something that looks a little bit like the swiss cheese models (where you have zones with different density profiles that each look like FRW, separated by voids). Each particular FRW like zone will eventually collapse under the assumptions of the LQC models, and each one will bounce in the usual way. Like that, the multiverse picture comes right back into play. Also b/c inflation is an exponential expansion of space, it was proved that it would quickly dominate the total volume of space regardless of details of the exact microphysics. Thus a typical observer is one that is either inflating, or has just finished inflating (at least if you base the measure on volume).

So the dilemma is the following. If you believe in only one bout of inflation, this necessarily implies that we happen to be right at the beginning of the universe (or alternatively that there is a conspiracy of initial conditions that forces exact homogeneity and isotropy during the late stages of FRW evolution). The former seems to violate the copernican principle, the latter is a finetuning of enormous degree.

 

[marcus]

I mean that the conditions for inflation are claimed to occur with high probability in a region of space after a specific set of conditions are met (after the bounce expansion phase).
http://arxiv.org/abs/1103.2475.

At this point, all you need is a sufficiently large volume of space and long enough time frames, and if you believe in unitarity physics, the same conditions *must* occur somewhere else. At the end of the day, its just a principle of quantum mechanics. Something that is not forbidden, will eventually occur, and occur infinitely many times given infinite time frames.

Now, its easy to see that the actual dynamics will look like the scenario that Bojowald describes. ...

I'm glad you mentioned Bojowald's recent paper.http://arxiv.org/abs/1212.5150 It opens up an entirely new line of investigation (as I see it.) It's interesting---I'll get to it in a moment.

First, though, you mention the 2011 Ashtekar Sloan paper arXiv:1103.2475, so I'd like to comment on that. As you say, Ashtekar Sloan argued that inflation in LQC is highly probable after an entire isotropic universe collapses and the bounce occurs, and the period of "superinflation" automatically entailed by the LQC bounce has occurred.

You say that by the "unitarity principle of quantum mechanics" the same specific set of conditions must occur infinitely many times in the future, namely the collapse of an entire universe etc.
That is a bit of a stretch. Frankly we expect our universe to continue expanding indefinitely and not collapse.

Tenuous abstract and a bit philosophical...in a trillion trillion years the second law of thermo might be violated too, and the entire universe undo itself, if you believe some philosophical premise about probabilities. But let's get back to reality:

In reality physics is based on approximate models and the excellent 2011 Ashtekar Sloan paper is just openers. Ashtekar has revised the way he models how the bounce prepares for inflation in some later papers, either with Sloan or with Agullo and Nelson. It is work in progress. I think its great work, fascinating. But I'm not ready to use THOSE putative conditions to extrapolate to a speculation about spontaneous occurrences a trillion years from now, or whatever.

And then we have Barrau Linsefors 2013 paper! this is explicitly to REDO the estimate of LQC bounce making adequate inflation highly probable, using a different approach from Ashtekar et al.
Barrau is explicitly going Ashtekar one better! That's also really interesting. It also assumes the collapse of an entire universe. To get the specific set of conditions you imagine occurring infinitely often.

So far we cannot extend this to black hole, collapse---the collapse of a finite region, not the whole entire universe. In LQG it has not yet been shown that BH collapse results in bounce. Different papers have drawn different conclusions. And only a beginning has been made including non-isotropy. There are some isolated papers that extend the bounce model to universes with limited types of anisotropy. Again, physics proceeds by successive approximation. We can look forward to increasingly realistic models, as simplifying assumptions of uniformity are gradually removed.

And then there is Bojowald's paper! This might just be a brilliant paper. I'm intrigued. He's on a highly individual track and it seems to lead him full circle. Several people have mentioned the Bojowald "LQC multiverse?" paper. I'll try to comment, but I also hope others who have read the paper and thought about it will comment as well.

Here's the link again for that December 2012 Bojowald paper, in case anyone hasn't seen it and wants to take a look. Be sure to check out the conclusions section at the end.
http://arxiv.org/abs/1212.5150

 

[Haelfix]

You say that by the "unitarity principle of quantum mechanics" the same specific set of conditions must occur infinitely many times in the future, namely the collapse of an entire universe etc.
That is a bit of a stretch. Frankly we expect our universe to continue expanding indefinitely and not collapse.

Tenuous abstract and a bit philosophical...

No! This is not a stretch, this is just the way unitary quantum mechanics always works, for any system (the universe is no exception). Namely if there exists a state psi that represents the state of the world prior to inflation, then there exists a Hermitian operator that takes any other state in the Hilbert space into psi.

Said another way, physics is reversible. This also means that the universe will not and cannot expand forever. Now, the timeframes where this can occur may or may not be ridiculously long, we don't know.. That depends on details of the microphysics that we do not understand.

What we do know for certain is that if you have immensely large volumes of space, then certain portions of the universe will eventually collapse. This will happen when the scales of the problem become such that you do not have perfect homogeniety and isotropy. At that point, there will be overdensities and underdensities, and some of those FRW worlds will exceed the critical value and undergo collapse in the way described by the LQC model.

Bojowald says the same thing here:
"A bounce, in general terms, may give rise to a multiverse picture, using the following line of arguments:
Consider a collapsing (part of the) universe. Inhomogeneity builds up as the universe evolves. If space is viewed as a patchwork of nearly homogeneous pieces, their size must be decreased after some time interval to maintain a good approximation, a mathematical process which can be seen as describing the dynamical fractionalization of space. These statements are true in any collapsing universe. If one uses a theory that gives rise to a bounce mechanism, denser patches that reach Planckian density earlier bounce first (assuming that homogeneous models are good for the patch evolution). These bounced patches appear as expanding regions embedded within
a still-contracting neighborhood. Given the opposite expansion behaviors, it is difficult to imagine that they can maintain causal contact with their neighborhood. A multiverse picture not unlike that of bubble nucleation in in-flation results, except that there is no analog of “bubbles
within bubbles” because a patch, once it has bounced, keeps expanding and diluting for a long time and would have to recollapse to trigger new bounces"

 

[marcus]

Hi Haelfix, I thought you might be thinking along those lines. Some notes of caution:

1. QM has not been successfully applied to the universe as a whole. Jim Hartle is just one who has written and given talks about how QM might be modified to work. It's not settled to everyone's satisfaction, perhaps not to anyone's

2. Bojo gives TWO scenarios, one at the beginning and one, after he as done his analysis, at the end. You quote the FIRST. And you draw a mistaken conclusion from it. Logically he does not say what you say because he describes BH collapse, the collapse of individual finite regions, and then he says "If one uses a theory that gives rise to a bounce mechanism..."

But LQG so far has not established BH bounce, various attempts have been made with various results. In what I've seen one can either get no bounce or one may come out missing a dimension, with a 1D or 2D expanding space. So Bojo is talking about using a "theory" that does not exist. the rest of what he says in the scenario is purely speculative and does not apply to LQG. So that gives no real multi prospect.

3. That's not his concluding scenario, however. What I really love about the paper, and believe may be brilliant, is what he gets to on PAGE 8 in the final section titled "Multiverse?".
This is is HIS scenario after he has done the analysis that is the reason for the paper, and it is remarkably different. Notice the question mark on the title of the section

If anyone else is reading this thread, I hope you will have a look at the final section of this paper, which Haelfix has helpfully called our attention to.
If you don't have the link handy, just google "bojowald multiverse" and you will get it.

Or just remember 1212.5150
because it's kind of an easy number to remember: "twelve-twelve fiftyone-fifty"
Bojowald is way out in left field at this point, a minority of one, but this is the sort of paper that is so different it could alter the discussion a bit. The idea is risky but possibly (if it finds confirmation) beautiful. It is partially based on some earlier work 1206.5765 he did with Paily.

 

[Haelfix]

Huh? I am discussing the first mechanism he lists which is decidedly not about BH formation. The second one is..

As for whether the universe and quantum mechanics are compatible. Well, its safe to assume that they are. In particular that unitarity holds is a safe assumption. Other's may or may not agree.

 

[marcus]

Huh? I am discussing the first mechanism he lists which is decidedly not about BH formation. The second one is..

The first mechanism requires one to imagine the collapse and bounce of a sub-region independent of the rest. I've never seen it shown that this happens in LQG. So he presents it as a hypothetical case "if you assume..."

We still have not gotten to his real message which is in the concluding section after he does his analysis. Have to go,back later

 

[Chronos]

Allow me to start by admitting I lack the mathematical fortitude to grasp the intricacies of Bojowald's paper. One thing that was unclear to me is his conviction that baby universe spawned by a bounce must be causally disconnected from the contracting phase. I followed the part where he explained how this was necessary to avoid entropy issues, but, failed to see any more rigorous explanation - albeit may have been staring right at me and I missed it. He also seems to imply all these bouncing baby universes are bounded and embedded in a very much larger, if not infinite, superverse. So effectively, this version of multiverse seems background dependent - which strikes me as rather odd.

 

[Haelfix]

That's correct Chronos, although what you call superverse, I call multiverse. I should note that the first mechanism that Bojowald describes is far from new, and essentially the same idea can be argued (and has been long ago) for the cyclic universe as well as many other classical bouncing (and even nonbouncing) variants.

Really the only thing that it hinges on, is the process of exponential expansion, as well as the premise that the total volume of the 'super'verse is enormous. If the 'super'verse is not enormous, you don't really get this picture and you can argue that homogeneity and isotropy that the initial bout of inflation generates is sufficient. (and then you also get into issues with the 2nd law, but that's another problem)

So if you want a picture of inflation that does not involve a multiverse, you really want conditions for the process to be extremely rare and involves a very low amount of efolding (which is at odds with various CMB conditions) and a large relic cosmological constant (also at odds with the fact that we are here). You also want a collapsing phase to occur not too long after the initial bout, so that causally separate horizons from FRW evolution do not have enough time to fluctuate too much so that thermal equilibrium is still a somewhat ok approximation.

 

[marcus]

Allow me to start by admitting I lack the mathematical fortitude to grasp the intricacies of Bojowald's paper. One thing that was unclear to me is his conviction that baby universe spawned by a bounce must be causally disconnected from the contracting phase. ...

Hi Chronos, the first thing to note here is that Bojowald is doing away with the LQC bounce and replacing it with something akin to "asymptotic silence", a breakdown of causal order, or if you like a temporary 4D Euclidean phase. His equations allow for a transition from classic GR's Lorentzian signature (- + + +) to Euclidean (+ + + +) and then back again to (- + + +).

This has similarities to Hawking Hartle no boundary, and to what is known as the BKL conjecture. And it sounds terribly hard, virtually impossible to understand. But maybe it is possible to get an intuitive feel for after all if we don't let it scare us.

It's refreshing because he is talking here about LQG (not the simplified LQC) and he is putting in all the inhomogeneity he can, and he is replacing the bounce by an episode of acausality.
.

In Euclidean 4D space you don't have light cones, you don't know who or what is in your causal past and you don't know what are the future events you can influence or communicate to. There is no causal ordering. Nothing can propagate! All structure is lost. All information is lost. The universe temporarily blanks out. And then according to his equations (the number β goes back to its earlier value and) Lorentzian signature comes back and causal order is restored and you have a new expanding phase of a new classical universe. And as he points out, despite what seems like a drastic change, there is no singularity.

It's possible that Bojowald is talking foolishness and his proposed model will be a fiasco. but I like it because it is so refreshingly different from all the LQC bounce papers I have read. So for now I'm going to try to follow his idea. Why shouldn;t we consider something different from a bounce (at the start of our expansion) just for a change?

there is a nice intuitive diagrammatic PICTURE in his reference [57] that helps me conceptualize.

I have to go run an errand by here are some links
http://arxiv.org/abs/1212.5150 (main Bojo paper)
http://arxiv.org/abs/1206.5765 (principle antecedent, with Paily, ref [58])
http://arxiv.org/abs/1112.1899 (the temporary Euclidean phase idea, with Paily,ref [12])
http://arxiv.org/abs/1212.3527 (the ref [57] with the intuitive picture, by Mielczarek)

 

[marcus]

Chronos, you mentioned seeing where he says (it comes up in Bojo's conclusions section on page 8) this temporary Euclidean causal stage is one way of addressing the ENTROPY puzzle. I don't think its the only convenient way, but it certainly is one obvious way to make it a non-issue. So that's nice.

You also mentioned how the loss of causal order (an increase in symmetry) at high energy is not intuitive so I want to point to Jakob Mielczarek's intuitive description. On page 1 he had Figure 1 that is kind of iconic for the idea and he describes it as a the kind of symmetry breaking that happens with the magnetic field as you cool something. Above a certain temp the magnetic field goes away because the field can't have a preferred direction. So things are more symmetric. But as the material cools below that temp, it can pick out a preferred direction and things are suddenly less symmetric. Euclidean 4D space has a big symmetry group because no lightcones, so one can think of that as how geometry is at very high energy but then as the temp cools it breaks down to Lorentz symmetry. a lesser amount of symmetry, a smaller group, because the lightcone structure somehow crystallizes at the lower energy density. Maybe I'm saying it clumsily. Here's how Mielczarek (Bojo ref [57]) says it:
==quote==
NATURE OF THE EUCLIDEAN PHASE
Based one above results one can speculate that the space-time is fundamentally Euclidean, and the Lorentzian structure emerges only in the limit of the low energy densities. In the high energy state (ρ > ρ_c/2), spacetime has no causal structure and the spatial and time directions are indistinguishable. Such a picture was, in fact, anticipated already in the early eighties of the last century by Hartle and Hawking in their famous no-boundary proposal [16]. The no-boundary proposal is based on the assumption that the Wick rotation gains the physical meaning at the Planck epoch. Our model replaces the sudden Wick rotation by the smooth change of the signature, with the intermediate state of the asymptotic silence. Such transition reminds phase transitions observed in solid states, and it is tempting to investigate such analogy in more details.
Let us focus on the model with the metamaterials composed of magnetized nanowires, which behave as spins [17]. Such nanowires are randomly orientated at high temperatures. While passing to the low temperatures, however, the wires align in a certain direction, spontaneously breaking the SO(3) symmetry of the system. The order parameter for the symmetry broken SO(2) ...
==endquote==
There's more, just click on his paper http://arxiv.org/abs/1212.3527 .

There's a critical energy density he calls ρ_c above which points lose causal contact with each other and the space-time becomes incapable of propagating anything. No lightcones so no waves. That's why Steve Carlip of UC Davis (and other people) call it asymptotic silence, neighbors can't hear each other, the world atomizes into private worlds. I recall Steve Carlip writing about "spontaneous dimensional reduction" of a bunch of quantum gravities, at small scale, and using this idea of asymptotic silence. He likes to compare different QG approaches and find common perceptions they share. Interesting that small scale geometry and high temperature geometry may be showing the same kind of 'atomization' and showing it across several QG approaches (CDT, AsymSafe, Horava, Loop, and I forget what others).

Anyway this is what Bojowald is suggesting to bring into replace the cosmological singularity, instead of the LQC bounce. And he thinks it's derivable in the context of inhomogeneous Loop cosmology by contrast to the bounce which is more at home in the simpler homogeneous isotropic LQC context. Sounds a bit on the wild side but if it's right it could be a valuable step forward.

Both Aurelien Barrau and Steve Carlip will be plenary speakers at Loops conference next month so their talks will presumably be online at Pirsa as video and slides PDF. Bojowald is registered to attend and will probably present a paper on this. So there should be a strong current of new ideas in the air next month about the what was happening at the start of expansion.