Origin of Quantum Perturbations?

[slatts]

There's a new paper by Barbour on Arvix, "Entropy and the Typicality of Universes".

It's not about an oscillatory model, but, per remarks that include note 18 on its p.10, it puts the transition from an expanding to a contracting phase, characteristic of such models, into the spacetime center of a multiverse with dual arrows of time, pointing in opposite directions, and seems to treat entropy as an emergent phenomenon. The math is way beyond me, but the diagrams suggest that the evidence centers around solutions to the three-body problem, which Wikipedia describes as soluble, but only through equations with 10^8,000,000th terms. (The problem was discovered in 1720, through some slight difficulties in figuring the relation between a planet having a satellite and the sun.)

Since I'm a procrastinator, I like multiverses without a beginning, but what I'm wondering here is whether any motion superimposed on the spatial expansion or contraction, on either side of the "Janus point" that Barbour uses to designate the boundary between the forward and backward flows of time, might've resulted in the quantum perturbations that cosmologists everywhere seem to take for granted. If it hasn't, any other explanation for them would be welcome.

 

[bapowell]

might've resulted in the quantum perturbations that cosmologists everywhere seem to take for granted. If it hasn't, any other explanation for them would be welcome.

What makes you say that cosmologists take quantum perturbations for granted? What about inflation?

 

[slatts]

What makes you say that cosmologists take quantum perturbations for granted? What about inflation?

I've found plenty of items about the perturbations developing into the structure of galaxies, but they don't seem to say why there were perturbations in the first place, or even (since I'm assuming they were fluctuations in the density of the potential for energy and matter) whether the particulate energy or particulate matter that appeared in the local endings of inflation was supposed to develop in the low-density portions of the fluctuations themselves, or in their high-density portions. Guth describes "thermal fluctuations" early in inflation, but, since temperature is a scalar, that would seem to leave them as abstractions that could be plotted on a graph but would not correspond to any observably physical reality until the motion of a (relatively) cool object into the higher range of their influence would release that potential through the Unruh effect. (I'm not saying that the Unruh effect was a factor in inflation, but I think it's a hypothetical effect supposedly consistent with inflation, that was dreamed up to help such incompletely-educated people as myself understand inflation.)

I believe that the author of a 1997 work (The Little Book of the BIg Bang)--that was endorsed by the Astronomer Royal--mentioned some controversy as to whether the fluctuations were "in" the inflaton field or pre-existing, and that, together with some drawings of wavy lines striking the outer sides of the metal plates in visual representations of the Casimir experiment, is about the only clear indicator I've been able to find that the primordial fluctuations might have had any spatial extent. In an earlier thread, you had described a change in terminology from "quantum perturbations" to "quantum fluctuations" that is usual in descriptions of that formation of particulate energy which is considered to have occurred upon such local endings of inflation as the one whose result was our "local" universe.

So, just assuming I got that right, let me ask whether the perturbations that preceded particle formation had any spatial extent, or any temporal duration, or both. Time is pretty slippery, but I'm guessing there's a consensus that they did at least have some spatial extent, and, if so, let me ask one further question in this post: Were they limited to the inflaton field? (On that, I'm guessing that there's still no consensus.) Thanks.

 

[bapowell]

The density perturbations generated by inflation are the result of inflation ending at different times in different places in the universe. Those places where inflation ended earlier reheat sooner, fill with matter sooner, expand at a slower rate than the those areas still inflating, and hence are more dense. The reason that inflation ends at different times in different places is that the inflaton is a quantum field, and fluctuations modulate the classical trajectory of the field. The perturbations are very much existing in space: we see them as CMB anisotropies.

Much of the work done through the 60's and 70's on gravitational particle creation that I believe you are referring to is not directly relevant to the generation of perturbations, although the formalism is similar. This is why modern treatments of inflation and large scale structure talk about inflation-generated quantum fluctuations rather than inflation-created particles.

 

[slatts]

,

The density perturbations generated by inflation are the result of inflation ending at different times in different places in the universe. Those places where inflation ended earlier reheat sooner, fill with matter sooner, expand at a slower rate than the those areas still inflating, and hence are more dense. The reason that inflation ends at different times in different places is that the inflaton is a quantum field, and fluctuations modulate the classical trajectory of the field. The perturbations are very much existing in space: we see them as CMB anisotropies.

Much of the work done through the 60's and 70's on gravitational particle creation that I believe you are referring to is not directly relevant to the generation of perturbations, although the formalism is similar. This is why modern treatments of inflation and large scale structure talk about inflation-generated quantum fluctuations rather than inflation-created particles.

This is very helpful and addresses my concerns very specifically, but there was a YouTube lecture by Vilenkin, on the occasion of Stephen Hawkings' 70th birthday (that would've apparently dated it in 2012), in which he mentions the inadequacy of the "emergent universe" (AKA "cosmic egg") hypothesis because the "egg's" instability under quantum fluctuations would've left its survival from an infinite past extremely improbable. Either in that lecture or in a comparably recent paper, he did use the Wheeler-deWitt equation--which I believe dates from 1967--in arriving at this conclusion, so do you think maybe he was giving that challenge to the BGV theorem (which requires a beginning for inflation) a brush-off that may've itself been out-of-date? (That lecture was actually my main reason for figuring that fluctuations occurring either outside the inflating region, or before inflation began, might've been considered a factor--even if one only remotely possible--in cosmology.)

 

[bapowell]

I think it's probably best to think separately about those two ideas: inflationary fluctuations in general and whether or not inflation is past eternal. In other words, we don't need to resolve the latter to work with the former. For example, we can perfectly well compute the spectrum of density perturbations from a given inflation model without worrying about when the inflationary phase started, so long as it began early enough to resolve the horizon/flatness problems.

 

[slatts]

Sounds like a good idea, but, just to be sure I got it right, you're saying that random fluctuations in the volume of space between pairs of quanta may've occurred a few times (or a few trillion times) before the larger one that Penrose claims would only occur every googol of years finally kicked in? (I can see that the big one would, because of its generic tendency toward perpetuation throughout the future, be the one likeliest to contain small fry like ourselves.)

 

[bapowell]

I'm not familiar with Penrose's claim. By inflationary fluctuations I am referring to spatial variations of the inflaton field energy (variations which have a quantum origin), not "random fluctuations in the volume of space between pairs of quanta".

 

[slatts]

Oh, right. There was a short thread called "Alan Guth, gravitationally repulsive material", started on Jan. 9 in 2014, in which you pointed out the fact that the inflaton is a scalar field of vacuum energy. In that thread, Chalnoth mentioned that, to initiate cosmic inflation, it would've had to have "an appropriate value across a region of space" of some minimum size. I'm glad you made clear, again today, that it's a special type of field. I guess that, at least on this side of Barbour's Janus Point, the pre-inflationary dregs that pro-procrastinators like myself are left with are just whatever less-than-appropriate values the inflaton may've had across smaller regions--as well as whatever non-scalar fields have been drifting around since forever.

Regarding Penrose (surely one of the most brilliant scientists of the past couple of centuries), I should also point out, for whichever of his fans might eventually look in on today's thread, that he does see inflation--exponential cosmic expansion--as a factor in a much broader-gauged, slower-moving cyclic cosmology of his own: In a temporally reversed re-enactment of the monkey accidentally typing Hamlet, I spent a perceptible fraction of an aeon plowing through his book Cycles in Time, and the "googol of years" remark was just a paraphrase of a remark of his, in one of the Wikipedia articles on inflation.

Thanks again for your help, and please let me know (seriously!) if I've gotten anything else wrong.

 

[spacejunkie]

Regarding Barbour's paper, it says they are restricting themselves to a classical model so I don't think that you can extrapolate anything quantum from it.

 

[Chronos]

Slatts, I feel the whole quantum perturbation thing is an illusion.

 

[bapowell]

Slatts, I feel the whole quantum perturbation thing is an illusion.

OK Chronos, I'll bite. Why??

 

[slatts]

Regarding Barbour's paper, it says they are restricting themselves to a classical model so I don't think that you can extrapolate anything quantum from it.

You're right as far as the work of Barbour and his collaborators in the paper at hand is concerned, but, on its page 32, he does claim that "Ashtekar and Sloan [in a 2011 paper on Arvix, called "Probability of Inflation in Loop Quantum Cosmology"] "had already noted how solution-determining data could be specified at a quantum 'Janus bounce', although apparently without recognition that it would give a one-past two-futures scenario."

 

[Chronos]

Perhaps we are tripping over words here. In the traditional sense a cosmological perturbation can be produced by a quantum fluctuation, but, the term quantum perturbation lacks definition. See http://www.worldscientific.com/doi/abs/10.1142/S0217732390002651 and http://arxiv.org/abs/hep-th/0405053 for discussion.

 

[slatts]

A recent paper on Arvix, co-authored by Carrol and called "De Sitter Space Without Dynamical Quantum Fluctuations", claims that any dynamical quantum fluctuations in de Sitter space require either "time-dependent histories of out-of-equilibrium recording devices" or "evolving microstates". Since "evolving microstates" seem much the likelier of the two, I'm hoping someone can tell me whether their evolution might be occurring on scales smaller than the Planck scale (whose observation I understand to be impossible on principle), or whether there's something in physics which rules that possibility out. Thanks.

 

[slatts]

Actually, since I have several questions about the paper co-authored by Carroll, my post #15 (together with #16, that I'm typing now) can be disregarded or deleted, and I'll start a new thread with those questions once I've gotten them formulated. It gets confusing for anyone to deal with two threads about the same paper. Sorry for the confusion, and I also regret having missed the "edit" window for deleting #15, although I guess it let's anyone who's just itching to answer it let their response fly...