Exploring Relation of Casimir Effect, Vacuum, Inflation & Dark Energy

[oldman]

I have trouble understanding how the Casimir effect, the vacuum, inflation, the cosmological constant and dark energy are related, if at all. My muddled understanding (which I'm hoping folk on this forum can clarify) is as follows:

The Casimir effect is a weak attraction between closely spaced metal plates. It’s been experimentally measured. The attraction is attributed to a deficit of long-wavelength zero-point energy modes of the confined vacuum of the electromagnetic field between the plates, compared with its unconfined vacuum outside.

The demonstrated existence of the Casimir effect proves that the vacuum of a field (i.e. Nothing at all) has energy.

In cosmology it is postulated that in the early universe there was a Field whose Vacuum had energy, and that this Field, which was derived from a Potential, could exist in a metastable state called the false vacuum, whose energy density was of the order of 10^81 Kg/m^3. The decay of the false vacuum into a lower energy state (the "true" vacuum) is postulated to have driven a exponentially rapid expansion, called inflation.

The cosmological constant, on the other hand, which might be assigned to vacuum field energy, now has an energy density of order 10^ (-31) Kg/ m^3, if it is indeed non-zero. And then there is the postulated but unidentified "dark" energy which helps to keep the universe flat, whose density is of a similar order of magnitude. It too might be vacuum energy.

But the huge discrepancies between the orders of magnitudes of vacuum energy and these other energies render such identifications impossible.

Now in the Standard Model it is agreed that, during the “ordinary” expansion of the universe, the density of mass/energy decreased from initially very high values to a present tiny average value.

Is it not then possible, during inflation, that (some of?) the (enormous) energy contained in the false vacuum, trapped as it was in the inflating universe, was similarly diluted during the many e-fold expansions of inflation, until it now masquerades as a (tiny) dark vacuum energy cum cosmological constant?

 

[Chronos]

Your bewilderment is shared by many scientists. The energy potential of the false vacuum is basically unlimited. Explaining why it was what it appears to be may be impossible. Bohm's 'many worlds' theory might be correct, IMO.

 

[marcus]

...The cosmological constant, on the other hand, which might be assigned to vacuum field energy, now has an energy density of order 10^ (-31) Kg/ m^3, if it is indeed non-zero...

that figure seems on the low side to me----of course I could be in error.

please let us know where you got it or how you arrived at it by converting from what commonplace estimate.

what puzzles me is if I convert to joules, by the factor 9E16
then I get 9E-15 joules per cubic meter

and that seems off by several orders, I am used to thinking of it as
6E-10 joules per cubic meter.

One of us seems to be off by 5 orders of magnitude. I hope it is not me!

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as for the core bewilderment, everyone is of course confronted with these same apparent discrepancies and there are different ways of coping.

my way is try to be realistic about the TRUTH STATUS of the different things.

1. inflation is just a SCENARIO not even a theory and the "inflaton" field is a stopgap imaginary gimmick.

2. casimir force is a real observed thing, and it does not depend on a set energy density but on an energy DIFFERENCE.

most energies in physics are on a sliding scale, you can peg the zero wherever you find convenient.

3. Gen Rel is due for a REVISION because it has singularities, places where it breaks. It will have to be quantized. there are already proposed MODIFICATIONS which offer to explain the observed acceleration without dark energy. One needn't take them seriously but they could prefigure the eventual revision.

4. Quantum Field Theory is due for revision because it is built on a fixed choice of background spacetime geometry-----a prior choice of spacetime metric. But Gen Rel teaches us that there is no such thing. It does not occur in nature and it is unphysical to assume it. QFT will have to be reconstructed without using a prior background geometry.

Interestingly this has already been done in 3D spacetime by two young French researchers Baratin and Freidel. they got Feynman diagrams of usual QFT in a backgroundless formulation. this has caused considerable interest. Baratin and Freidel are working on the 4D spacetime case and are expected to post a new paper sometime this year.

Many things are likely to change when there is a backgroundless QFT or, as one might say, a GENERAL RELATIVISTIC QUANTUM FIELD THEORY.

at present QFT is only specialrelativistic. it does not conform to Gen Rel. the "Standard Model" of particles arises from this not-fully-relativistic QFT. when there is a fully relativistic QFT one would expect some resolution of problems with the "Standard Model"---some kind of reformulation or renovation.
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so I think the way to resolve these apparent discrepancies (at least for me) is simply to take account of their different levels of reliability.
I am happy to TAKE REAL MEASUREMENTS SERIOUSLY like the casimir and the supernova data on acceleration and the CMB and galaxy rotation curves etc.

On the other hand some of the other stuff is just SCENARIOS which are all right for the time being until the basic models are revised.

And some of the other numbers might be ARTIFACTS of particular models that one has to admit are approximate and provisional and in dire need of revision because they BREAK or are based on UNPHYSICAL ASSUMPTIONS-----like Quantum Field Theory and Gen Rel have to be viewed as provsional approximate effective theories due for overhaul.So one can just kind of smile ruefully when one hears Particle Theorists squawk because their (inadequate) QFT predicts a huge Planck energy density instead of the (pretended observed) "dark energy". While the real Cosmologists are not even sure they believe in "dark energy"---all they can actually see is the flatness and the acceleration----to keep their provisional model limping along requires a kludge and "dark energy" is their temporary fix. It is just a make-do patch. Both models need a basic overhaul so the fact they have a discrepancy between their highly dubious numbers is no big deal.

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that's my take on it. Different people resolve it for themselves in different way. My adjustment to the situation is just my own personal way of adapting, and I don't urge it on anyone else.

For me, it means that I watch Baratin and Freidel about backgroundless QFT. I watch Ashtekar and Bojowald about the quantum black hole and the beginning of expansion (no longer a bang). I watch the versions of MOND by Bekenstein and by Moffatt, which are making testable predictions. In other words, I watch the fragments that look like they are coalescing into a new picture.

BTW although I speak disparagingly of the TRUTHVALUE of the Inflation SCENARIO, I personally suspect that some kind of inflation picture is right----and partly this is because Inflation surprised everybody by turning out to be GENERIC in Loop Quantum Cosmology (Bojowald, Ashtekar). It happens without anybody asking, and to some extent even without a specialized "inflaton" field. And conditions near the bounce are so extreme that any QFT you use to talk about an "inflaton" SHOULD BE A FULLY RELATIVISTIC QFT.
the space near the bouce is very far from flat. Applying a QFT built on flat specialrelativistic Minkowski space to that situation seems kind of dubious. So the basic idea of inflation may be OK (I suspect it is!) but our models of it are bound to change quite a lot as we begin to acquire the tools of quantum Gen Rel, and fully relativistic QFT.

Remember that a fully relativistic QFT is exactly what the Baratin Freidel April 2006 paper is about.
Why don't you have a look at it, oldman? http://arxiv.org/abs/gr-qc/0604016
Just skip the middle and read their intro and their conclusions.

 

[SpaceTiger]

The demonstrated existence of the Casimir effect proves that the vacuum of a field (i.e. Nothing at all) has energy.

I wouldn't call a vacuum "nothing at all", but that's correct.

And then there is the postulated but unidentified "dark" energy which helps to keep the universe flat, whose density is of a similar order of magnitude. It too might be vacuum energy.

"Dark energy" is a more general term for energy components that cause the universe to accelerate. It could be the cosmological constant or it could be something else (like quintessence).

But the huge discrepancies between the orders of magnitudes of vacuum energy and these other energies render such identifications impossible.

The magnitude of the vacuum energy has not actually been measured, the only existing evidence is based on energy differences. There appears to be a discrepancy between the predicted vacuum energy and the measured cosmological constant, but that is based only on a naive integration to the Planck scale (this is called the "fine-tuning problem"). None of these things are thought to be related to the inflaton potential of the early universe.

Is it not then possible, during inflation, that (some of?) the (enormous) energy contained in the false vacuum, trapped as it was in the inflating universe, was similarly diluted during the many e-fold expansions of inflation, until it now masquerades as a (tiny) dark vacuum energy cum cosmological constant?

In fact, most of the energy built up in the inflaton potential did become diluted, but not in the form of a cosmological constant. In an epoch we call "reheating" (after inflation), most of this energy was dumped into light and matter, which then became diluted as the universe expanded.

A cosmological constant, however, is true to its name and retains a constant energy density as the universe expands. I suppose it is possible, however, that some of the inflaton potential's energy was dumped into a quintessence field, which we now see as the dark energy.

 

[oldman]

Your bewilderment is shared by many scientists.

Yes, I suspected that it might, but it is reassuring to know that I'm not alone in my foolishness. I hope that in the not-too-distant future some kind of resolution of these matters will emerge. The knowledge-horizon, as it were, has been pushed back a long way in the last few decades, but its character is frustratingly reminiscent of the Omphalos cosmology that I poked fun at in another thread, where the scene for physical evolution is set by fiat, as it were.

I also hope that the quote from Oliver Lodge that ends all your posts does not apply too strictly to us. By the way, where does it come from?

please let us know where you got it or how you arrived at it by converting from what commonplace estimate... One of us seems to be off by 5 orders of magnitude. I hope it is not me!

It's not you. I got it from Penrose's Road to Realitysection 28.4 "density about .. 10 ^ - 30 that of water" and then used the wrong density of water. I hate myself for this!

Then:

1. inflation is just a SCENARIO not even a theory and the "inflaton" field is a stopgap imaginary gimmick.

I agree, and believe that the inflaton field is an example of Omphalos cosmology (I love that word; so pompous!).

2. casimir force is a real observed thing, and it does not depend on a set energy density but on an energy DIFFERENCE.

most energies in physics are on a sliding scale, you can peg the zero wherever you find convenient.

Yes indeed. The points 3 and 4 you made about the need for GR and QFT to be revised are well taken. Roll on the Millennial physics revolution. It's overdue.

...the real Cosmologists are not even sure they believe in "dark energy"---all they can actually see is the flatness and the acceleration----to keep their provisional model limping along requires a kludge and "dark energy" is their temporary fix. It is just a make-do patch.

I also like the outlook you've sketched above and elsewhere in your post. It's nice and pragmatic. Just one aside: is the acceleration by now well-established? I've only to hand the deviation from a straight line drawn in Fig. 10.7 of Kirshner's The extravagant universe which didn't look vastly convincing ... but that was 2002; this is now...

Thanks for pointing me at the Baratin and Freidel paper. It's a bit stratospheric for my atrophied intellect, but I am glad to know that folk working in Ontario are at the cutting edge, as it were.

I wouldn't call a vacuum "nothing at all"

I took this from Peacock's ending to his chapter on inflationary cosmology in Cosmological Physics: "It is perhaps just as well that the average taxpayer, who funds research in physics, is unaware of the trouble we have in understanding even nothing at all". An apt summing up!

In fact, most of the energy built up in the inflaton potential did become diluted, but not in the form of a cosmological constant. In an epoch we call "reheating" (after inflation), most of this energy was dumped into light and matter, which then became diluted as the universe expanded.

Yes, I am aware of this. But nevertheless thanks for your response to my rather crazy suggestion:

A cosmological constant, however, is true to its name and retains a constant energy density as the universe expands. I suppose it is possible, however, that some of the inflaton potential's energy was dumped into a quintessence field, which we now see as the dark energy.

 

[SpaceTiger]

I agree, and believe that the inflaton field is an example of Omphalos cosmology (I love that word; so pompous!).

At what point does a cosmological theory cease to fit your definition of "Omphalos cosmology"? How few initial parameters must it have? With what level of fine-tuning? Inflation was certainly an attempt to reduce the amount of fine-tuning in cosmological models. Of course, it would always be nice to have an explanation for the origin of the inflaton field, but then one can ask "why?" for any physical theory, no matter how fundamental.

I also like the outlook you've sketched above and elsewhere in your post. It's nice and pragmatic. Just one aside: is the acceleration by now well-established? I've only to hand the deviation from a straight line drawn in Fig. 10.7 of Kirshner's The extravagant universe which didn't look vastly convincing ... but that was 2002; this is now...

The combination of WMAP, SNe, and large scale structure data (among other things) has convinced the vast majority of the astronomical community that the universe is accelerating.

I took this from Peacock's ending to his chapter on inflationary cosmology in Cosmological Physics: "It is perhaps just as well that the average taxpayer, who funds research in physics, is unaware of the trouble we have in understanding even nothing at all". An apt summing up!

I've always preferred the quantum point of view:

In modern physics, there is no such thing as "nothing." Even in a perfect vacuum, pairs of virtual particles are constantly being created and destroyed.

It's mostly a semantic point, though.

 

[oldman]

At what point does a cosmological theory cease to fit your definition of "Omphalos cosmology"? How few initial parameters must it have? With what level of fine-tuning? Inflation was certainly an attempt to reduce the amount of fine-tuning in cosmological models. Of course, it would always be nice to have an explanation for the origin of the inflaton field, but then one can ask "why?" for any physical theory, no matter how fundamental.

I take the point that inflation is an attempt "to reduce the fine-tuning" of cosmological models, and agree that it is necessary to always strive towards this end. I have been convinced, though, by one of the points made by Penrose: that "inflationary cosmology... (does) ... not resolve the cosmological problem that overshadows all other, namely the extraordinary 'special' Big Bang --- to at least the degree of a part in 10^10^123 --- which underlies the Second Law." (His section 28.10-- The Road to Reality").

Hence I refer to "Omphalos cosmology" to stress that no matter how far the knowledge horizon is pushed back in this way, we still seem to be stuck with the problem that, rather like Philip Gosse's (now comical) suggestion: the universe is assumed to start as a "given" construct, equipped with all that is needed for its subsequent evolution.

I confess that I still hanker after the old "bootstrap" idea , which says that things are as they are because that's the only way they could fit together. But I suppose this is only a matter of my prejudice.

The combination of WMAP, SNe, and large scale structure data (among other things) has convinced the vast majority of the astronomical community that the universe is accelerating.

Thanks for this reassurance.

I've always preferred the quantum point of view...It's mostly a semantic point, though.

Agreed. And I accept both points of view.

 

[Chronos]

I agree the standard model is difficult to digest, but not demonstrably wrong. On the other hand, I think you need new, or modified field equations to refute it [the concordance model] - that's what I'm looking for, and what I expect from any competing model.

 

[oldman]

I agree the standard model is difficult to digest, but not demonstrably wrong. On the other hand, I think you need new, or modified field equations to refute it [the concordance model] - that's what I'm looking for, and what I expect from any competing model.

The standard model (which has now metamorphosed into the lambda-CDM model?) may be difficult to digest; but it is very credible in the detailed understanding it provides for observed features of our universe. A prime example of this is a recent paper by Li and many others: http://arxiv.org/abs/astro-ph/0608190 in which the formation of supermassive black holes at high z is convincingly simulated. To me this looks pretty good supporting evidence for the model and, in particular, dark energy.

And yet the invention of devices like inflation, dark matter and dark energy seem so like special pleading, while the initial state of the universe remains so mysterious, that I suspect that the model's foundations are not yet entirely sound.

Maybe it's the field equations, as you comment, Chronos. But more simply; what about the metric? Cosmologists have over the years devoted much time and effort in explaining to the uninformed why and how space sections can be curved, only to find that the universe is flat after all. Meantime, expansion -- the absolute essence of the current consensus -- is too often briefly dismissed with ex cathedra statements. I find changes of scale far more tricky to understand than curvature. Gauge matters!

 

[Chronos]

The field equations are the metric. Predicting the geometry of the universe over time is the problem. It is no less surprising the universe appears flat at this moment in cosmological time than that it appears flat at any moment in cosmological time.