Is "heavy nothing" already infinite or is it expanding?

[slatts]

I need some help from people who can read the math in papers by such physicists as Linde. In his 2014 paper (on the web) "Inflationary Cosmology after Planck 2013", he says,

"False vacuum is a metastable state without any fields or particles but with large energy density. Imagine a universe filled with such 'heavy nothing'. When the universe expands, empty space remains empty, so its energy density does not change".

First, I'm hoping to confirm that Linde is referring only to the density of potential energy, AKA the potential for energy (whose potential I figure to always have some density vis-a-vis volume, at least in any regions of generic space that our remotest descendants might eventually reach). I've formulated this guess partly because Linde is pretty down-to-earth in his use of English, and partly because he seems to be talking about a time before the fluctuations in the inflaton had reached those regions of "heavy nothing", when the Unruh effect could not yet have set any jet-packing space cadet's hair on fire.

Second, since I myself have brainlessly breezed through the non-mathematical parts of Ali & Das' 2014 "Cosmology from Quantum Potential" (-also on the web, and very ably discussed in a couple of long PF threads) and want to prepare myself for the possibility that they might even be right about the universe already having an "infinite age", I'd like to know whether an "open" universe is generally considered to be "open" because the aforementioned gravitational field is already infinite spatially, or only because the parts of the inflaton that have already blasted through OUR region WILL reach all of the spatial regions already reached by that gravitational field LONG before we or any of our descendants ever could (-even by riding the inertial expansion of our own bubble, whose expansion is of course the fastest thing in these parts).

Thanks.

 

[PeterDonis]

Linde. In his 2014 paper (on the web) "Inflationary Cosmology after Planck 2013

I assume you mean this paper:

http://arxiv.org/abs/1402.0526

I'm hoping to confirm that Linde is referring only to the density of potential energy

He is talking here about the ground state energy density of the "false vacuum" state of the inflaton field, in the "old inflation" model; i.e., the energy density that is present due to the vacuum expectation value of the inflation field. Whether you want to call this a "potential energy" is a matter of terminology; the important point is that it's the only energy density present in this state.

Also, you should note carefully that this part of Linde's paper is discussing the "old inflation" model, which is not considered viable any more; in fact, Linde says so explicitly in the very next paragraph after the one you quoted from.

he seems to be talking about a time before the fluctuations in the inflaton had reached those regions of "heavy nothing

I'm not sure what you mean here. Quantum fluctuations in the inflaton field are everywhere in this model; they don't start from one place and spread out. The energy density Linde is referring to is the average energy density, i.e., after averaging over the fluctuations.

when the Unruh effect could not yet have set any jet-packing space cadet's hair on fire.

What does the Unruh effect have to do with any of this?

I'd like to know whether an "open" universe is generally considered to be "open" because the aforementioned gravitational field

What "aforementioned gravitational field"? You haven't said anything yet about any gravitational field.

 

[slatts]

I'd had no idea that Linde was referring to the ground state of the inflaton. I'd thought he was referring to the gravitational field, because many popularizations claim that the energy of inflation is provided by gravitation.

Please let me know if I'm right in assuming that the ground state is the state of lowest energy density, and if most physicists would usually equate that to a potential. I alluded to the Unruh effect because it had been my impression, from a reading of Smolin's Three Roads to Quantum Gravity, that only acceleration (-for instance, of an astronaut speeding up) would activate that potential.

I'd assumed that the graviton and inflaton fields would be superpositioned, and that the regions occupied by them would only overlap, with the graviton being more extensive spatially and perhaps generally older temporally, albeit only in some sense only very approximate, within SR approximations of GR. (I realize that, so close to the quantum level, space and time might be almost indistinguishable, but I'm not sure how much that indistinguishability would divide the inertial frames or increase their number.)

When Linde had started to discuss the failure of Old Inflation, I'd figured he was going to elaborate on the bubble collisions which Guth had claimed accounted for it, and had hoped that the background Linde had described would stand. (When Guth, in his own 1991 popularization, had described the constant density of the expanding universe without elaborating on the reason for it, its massive field had sounded like a gigantic particle, and this matched Linde's description of an energy density lacking fluctuations or particles-in-the-plural.)

 

[slatts]

I've been trying to get through the Linde paper to see whether contraction due to cooling in slow-roll inflation might, as in "old" inflation, comprise the tension or "negative pressure" making gravity repulsive and "driving" inflation.

 

[PeterDonis]

I'd thought he was referring to the gravitational field, because many popularizations claim that the energy of inflation is provided by gravitation.

This is a good example of why you shouldn't try to learn science from popularizations.

Please let me know if I'm right in assuming that the ground state is the state of lowest energy density

Yes, by definition.

and if most physicists would usually equate that to a potential

No, certainly not. The potential is a term in the Lagrangian; the ground state of the field is the lowest energy solution to the field equations.

If you are not familiar with quantum field theory, you should take some time to learn the basics. Without that background you will have great difficulty following discussions of inflationary theory.

I alluded to the Unruh effect because it had been my impression, from a reading of Smolin's Three Roads to Quantum Gravity, that only acceleration (-for instance, of an astronaut speeding up) would activate that potential.

I haven't read Smolin's book, but I would be extremely surprised if he intended that implication; it's certainly not correct. Nobody postulates that the presence of an accelerated astronaut was required to trigger inflation, or to trigger the end of inflation.

I'd assumed that the graviton and inflaton fields would be superpositioned...

This paragraph is all ungrounded speculation which has nothing to do with inflationary theory. Again, I think you really need to take some time to learn the basics of quantum field theory, and then re-read Linde's paper (which, AFAICT, gives a good overview of the various kinds of inflationary theories that have been proposed) with that background.

When Linde had started to discuss the failure of Old Inflation, I'd figured he was going to elaborate on the bubble collisions which Guth had claimed accounted for it, and had hoped that the background Linde had described would stand.

No, it doesn't. Linde's main point in that portion of the paper, as far as I can see, is that the entire conceptual framework of "old inflation" and "new inflation", talking about bubbles forming via a phase transition from a supercooled "false vacuum" state to a hot "Big Bang" state, is not a good conceptual framework to understand the inflation theory candidates that are actually viable.

contraction due to cooling in slow-roll inflation

What contraction? There isn't any; the universe is expanding exponentially during the slow-roll phase.

(Even in the ordinary case of an ideal gas, cooling does not imply contraction; a gas cools as it expands, and heats up as it contracts.)

 

[slatts]

Peter Donis said, "If you are not familiar with quantum field theory, you should take some time to learn the basics. Without that background you will have great difficulty following discussions of inflationary theory."

Maybe you could recommend a book. Susskind has one on QM that starts pretty comprehensibly, but he says it requires "some basic calculus", so I checked out an extremely basic one on that.

Peter Donis said, "I haven't read Smolin's book, but I would be extremely surprised if he intended that implication; it's certainly not correct. Nobody postulates that the presence of an accelerated astronaut was required to trigger inflation, or to trigger the end of inflation."

Oh no, he wasn't talking about any human (or other, or Other) intervention in inflation; in fact, he wasn't even talking directly about inflation. He was just describing the effect of a rocket pilot accelerating continuously to stay permanently ahead of photons that were a certain large distance behind him: As the pilot's velocity was asymptotically approaching theirs, I guess Smolin was right that an invisible horizon would effectively separate them, and that, since those photons would have been entangled with some on the pilot's side of that horizon, their motion would have been random to him and his rocket, and would have consequently heated up a thermometer it contained. (It somehow makes intuitive sense that particles in random motion would generate some heat in objects they strike.)

Smolin was relating this phenomenon to the horizons around black holes, but I imagine there would be a similar effect even aboard a hypothetical rocket in the inflating region, impossible though any travel there will always remain. I know that the particle theorists' possible Grand Unified Vacuum, and maybe even their probable Electroweak Vacuum, were at some phenomenally high temperatures, and, even though I think that each of those false vacuums endured (per our time) for only the finest shaving of a split second, I'm assuming that it would've sufficed to evaporate the pilot instantaneously, even if he had felt sure it was absolute zero outside for quite some time until he'd fired his jets.

I believe Smolin was talking about the Unruh effect. His story did inspire me to ask about the colloquial use of "potential". (Until last summer, I thought Lagrange was just a town in Indiana.)

Peter Donis said, "What contraction? There isn't any; the universe is expanding exponentially during the slow-roll phase. (Even in the ordinary case of an ideal gas, cooling does not imply contraction; a gas cools as it expands, and heats up as it contracts.)"

Is that the case even if the gas is in a container? (In his book about time, Bojowald said something about the contraction of a cooling substance in a container resulting in the sort of tension or negative pressure that, per Einstein's equations relating pressure and volume to gravity, have been said to make gravity repulsive.) Or is it possible that the contracting material is not a gas? ( In asking these last two questions, I'm wanting to verify in what sense that often-cited piece of the Einstein equations might still be considered basic to inflation, or even relevant to it.)

 

[PeterDonis]

I imagine there would be a similar effect even aboard a hypothetical rocket in the inflating region, impossible though any travel there will always remain.

I understand what the Unruh effect is. What I don't understand is why someone in an accelerating rocket would be needed to "activate the potential" in the inflaton field. There don't need to be any accelerated objects for inflation to start or stop.

Is that the case even if the gas is in a container?

If the gas is in a container, how can it contract or expand? Its volume is determined by the volume of the container. Its pressure and temperature can change, but its volume can't.

is it possible that the contracting material is not a gas?

Remember that the gas example I gave was not intended to have anything to do with inflation. In inflation, there is no "contracting material" at all. See below.

I'm wanting to verify in what sense that often-cited piece of the Einstein equations might still be considered basic to inflation

Of course it is. The inflaton field has an equation of state $p = - \rho$, i.e., its pressure is minus its energy density. That causes accelerating expansion.

 

[slatts]

I understand what the Unruh effect is. What I don't understand is why someone in an accelerating rocket would be needed to "activate the potential" in the inflaton field. There don't need to be any accelerated objects for inflation to start or stop.

You're right, of course. Sorry, I don't know why I was thinking that the inflaton--our outer space's outer space--would be just like our outer space; I've got a good memory, but it goes (in my case) with a lack of category boundaries that's almost schizophrenic, and leads to logical problems similar to dyslexia. (Just apologizing in advance, here, for why I'm doubtful that any amount of math and QM study will keep me off your case load.)

Of course it is. The inflaton field has an equation of state $p = - \rho$, i.e., its pressure is minus its energy density. That causes accelerating expansion.

Got it! Alright! Thanks very much!