I "Dark energy" may be nothing more than baseline curvature

[marcus]

There is a lot of research interest in different variants of GR, UG might or might not turn out to be the right alternative.
I think the main thing to remember is that when we measure the cosmological constant what we actually measure is the baseline expansion rate
H_∞ ≈ 1/173% per million years.
The current expansion rate is on a glide path down towards, and leveling out at, that rate. We can derive its history from redshift-distance observations, and see where it is heading, asymptotically.

So in a practical straightforward way, since that is what we observe and measure that is what the CC is. Express it either as the baseline expansion rate or as the baseline constant spacetime curvature which that corresponds to. Connecting that curvature to an imagined "energy" merely is speculative. Assuming vacuum energy must contribute to the curvature constant is an entrenched prejudice, not something proven scientifically. It involves questionable and often unstated assumptions.

 

[Chronos]

I concur the curvature constant is the gorilla in the room, but, I find it difficult to deny vacuum energy offers a tantalizing carrot to explain the lamb shift and casimir effect. Perhaps the truth lay somewhere in between.

 

[Haelfix]

Yes, so Unimodular gravity is certainly an interesting idea and a viable research direction. It is extremely illuminating to understand in what sense it actually ameliorates the problem, b/c it is actually subtle and not exactly agreed upon in the literature.

Here is what it doesn't solve. It doesn't explain the finetuning of the cosmological constant, which is so far from its natural value. It also doesn't resolve this aforementioned problem where you need to keep the 'fast modes' which we observe gravitating (eg the Lamb shift, the mass of nucleons and QCD) all the while severing the link between the 'slow modes' (eg the vacuum) and the thing that affects cosmological scales. That still needs an explanation.

On the other hand, it does in some sense help (controversially) b/c you no longer have to explain a hierarchy of scales. It becomes just one boundary value problem to explain, and you don't in principle need to explain the incredible conspiracy between all scales of physics.

However, details here are not universally agreed upon. For as long as I've known about unimodular gravity, the experts have gone back and forth on whether or not it is really different than GR in the quantum regime. Very subtle gauge issues exist here along with the exact methodology in quantizing a constrained system that has partial general coordinate invariance. The right answer is to shut up and calculate (see the Ellis paper), but it is quite hard and as usual the worry is that you can't be quite sure about what shows up at subsequent loops, as well as what perturbation theory misses.

Anyway, its worth emphasizing though just how radical this idea really is for physics. You are throwing out a symmetry of nature (diffeomorphism invariance) and inventing an entirely new theory that presumably will have very different properties in the quantum regime (so throw out everything you know about black hole physics, early universe physics, the physics of semiclassical gravity would need to be reworked and so forth). But that's the level of difficulty you are looking at when you attempt to solve the cosmological constant problem, there doesn't seem to be any facile way of getting around the problem.

 

[Haelfix]

So in a practical straightforward way, since that is what we observe and measure that is what the CC is. Express it either as the baseline expansion rate or as the baseline constant spacetime curvature which that corresponds to. Connecting that curvature to an imagined "energy" merely is speculative. Assuming vacuum energy must contribute to the curvature constant is an entrenched prejudice, not something proven scientifically. It involves questionable and often unstated assumptions.

We certainly measure something, and that something is indistinguishable between either hypothesis. Theoretically it is much, much easier to believe that vacuum energy is the culprit, simply b/c our prejudice is to believe there exists an exact quantum theory of gravity (by this I mean you can promote Einstein's equations to an operator equation). If that is true (and again, it might not be if you modify GR) then by Lorentz invariance, the vacuum must gravitate (the expectation value of the stress energy will give a contribution that is exactly the same as the cosmological constant). It is so simple that its hard to see what goes wrong, and that's why such a plurality of scientists prefer this explanation. Further in some sense it makes no difference which hypothesis you prefer, b/c even if you think the ultimate explanation is decoupled from the matter part of the equations, the same exact dangerous renormalizations take place on the curvature side of things, so it seems merely a matter of bookkeeping.

 

[marcus]

... there exists an exact quantum theory of gravity (by this I mean you can promote Einstein's equations to an operator equation). If that is true (and again, it might not be if you modify GR) then ...

Scientifically speaking it is an open question whether to promote the original Einstein GR equations or one of several variants being studied that are equivalent at a classical level. As the George Ellis et al paper points out, one has to be able to distinguish observationally. Glad to see you explicitly stating assumptions that might otherwise have crept in unannounced.

We don't KNOW that vacuum energy gravitates. So the simplest thing is to treat the CC as baseline curvature---pending an observationally confirmed QG theory.

 

[marcus]

I concur the curvature constant is the gorilla in the room, but, I find it difficult to deny vacuum energy offers a tantalizing carrot to explain the lamb shift and casimir effect...

Nobody denies the existence and interest of vacuum energy. Everybody loves Lamb shift and Casimir effect. The issue is whether or not it GRAVITATES. In some variants of GR it does contribute to baseline curvature, in some it does not.

Intuitively, since it is the same everywhere and at all times, it doesn't NEED to contribute to spacetime curvature---and there are various ways to implement that being actively studied. I'm with you on supporting Casimir effect Lamb shift and all, but that's a separate issue. : ^)

 

[john baez]

Marcus said:

It might eventually turn out to be related to some type of energy. That's possible. But so far there seems to be no reason to imagine that it is is connected with anything we'd normally consider an energy---it is simply the universe's baseline curvature in the absence of matter.

As others have said, it's just a matter of interpretation whether you want to treat the cosmological constant term in Einstein's equations as part of the energy-momentum tensor or just... some other thing, which you're calling "baseline curvature". This decision doesn't affect any predictions. Of course, if we treat it as part of the energy-momentum tensor, we might want to try to explain it as the result of some more complicated and interesting phenomenon. If we treat it as "baseline curvature", we can, presumably, be happy without seeking any deeper explanation.

Since we don't understand it well, we should investigate both alternatives. But since one alternative says "don't bother trying to understand it: it just is what it is", physicists will naturally spend more time on the other alternative. Not because it's more likely to be right, just because it gives them more to do.

 

[john baez]

QFT says that vacuum must have some intrinsic energy.

In brief: no. It could have some intrinsic energy, but in most familiar quantum field theories (QED, the Standard Model) the energy is assumed to be zero.

 

[strangerep]

Since we don't understand [the cosmo constant] well, we should investigate both alternatives. But since one alternative says "don't bother trying to understand it: it just is what it is", physicists will naturally spend more time on the other alternative. Not because it's more likely to be right, just because it gives them more to do.

This reminds me of old attempts to account for a universal speed of light constant via aether models, trying to show how the aether presents more and more resistance to motion, such that a speed limit is eventually reached.

 

[marcus]

I just got alerted that Student100 liked this post (#9 of this thread) so maybe it says some things in a good way that communicates, and I should expand on it. Here's the post:

You couldn't do better than read the Bianchi Rovelli paper and paraphrase that in summary, rather than paraphrasing what I said. But yeah. If spacetime geometry exists, i.e. if spacetime exists, then it has some inherent curvature. No reason that should be zero. It has to have some inherent intrinsic baseline curvature, if it exists. So you don't have to make up anything. It is forced on you.

If you want to speculate that it "comes from" some kind of "energy", then you have to
1. postulate that the baseline inherent curvature is ZERO and then
2. you have to make up some "vacuum energy" that bends the spacetime just the right observed amount.

Nothing like that has been calculated starting from an accepted theory of qg. One would not want to start from MINKOWSKI space the way e.g. QFT people do.
Any "vacuum energy" you calculate based on Minkowski space (not quantum, i.e. not realistic geometry) is just silly. And you can see it gives a silly answer many OOM off the mark.

Simplest thing is just to not make anything up. Spacetime behaves as if it has a basic baseline curvature prior to anything else affecting it. So accept that.
It has been measured, it seems constant at a definite value. Like Planck's constant.

I'll try to think what more to add, along these lines.

 

[marcus]

...
As others have said, it's just a matter of interpretation whether you want to treat the cosmological constant term in Einstein's equations as part of the energy-momentum tensor or just... some other thing, which you're calling "baseline curvature". This decision doesn't affect any predictions. Of course, if we treat it as part of the energy-momentum tensor, we might want to try to explain it as the result of some more complicated and interesting phenomenon. If we treat it as "baseline curvature", we can, presumably, be happy without seeking any deeper explanation.

Since we don't understand it well, we should investigate both alternatives. But since one alternative says "don't bother trying to understand it: it just is what it is", physicists will naturally spend more time on the other alternative. Not because it's more likely to be right, just because it gives them more to do.

This is a very interesting post. It reminds me of a recent paper by Sakellariadou and two other people where they show how an effective constant baseline curvature could arise. (Depending on whatever the energy density happened to be at Planck time.)
1. arXiv:1603.04170 [pdf, other]
Effective cosmological constant induced by stochastic fluctuations of Newton's constant
Marco de Cesare, Fedele Lizzi, Mairi Sakellariadou
Comments: 10 pages, 1 figure

2. arXiv:1603.01764 [pdf, other]
Accelerated expansion of the Universe without an inflaton and resolution of the initial singularity from GFT condensates
Marco de Cesare, Mairi Sakellariadou
Comments: 4 pages, 4 figures

They do seek a deeper explanation, as you say. They set up a model and use it to explain the effective cosmological constant in a way that puts constraints on what we can say about conditions in the very early universe. But it's a different kind of explanation from the usual attempt that involves today's QFT vacuum energy. Several things (not only Lambda but Newton's constant itself) arise out of random fluctuations at the start of expansion, in their model.

 

[marcus]

==quote page 8 arXiv:1603.04170 last paragraph before Conclusions section==
In other words, the effective cosmological constant depends on the initial value of the total energy density, but not on the species populating the Universe. It seems natural to fix the initial data at a time where all species where equally dominating, i.e. t_i ≈ t_Pl. This conclusion, if correct, due to the limits of our effective approach at Planckian times, implies that the final stage of evolution of the Universe is entirely determined by quantum fluctuations of the spacetime geometry at early times. Furthermore, being determined only by the initial value of the total energy density, it treats all fields on the same level and it is insensitive to further details of the Universe’s history. In this sense Eq. (18) can be interpreted as a constraint on the underlying quantum theory, at the time when the dynamics of the fast degrees of freedom of the gravitational field approach their stochastic limit.
==endquote==

The value of the Newton constant ALSO arises from conditions at the very start, according to their analysis. It's not as crazy as it might seem IMHO. I started a thread about it in BtSM forum:
Effective cosmo const explained w/o matter vacuum energy
https://www.physicsforums.com/threa...st-explained-w-o-matter-vacuum-energy.862154/

 

[.Scott]

Wouldn't that still leave the possibility that the cosmological constant is a cosmological function of time?

Not directly. If it's a function of time, we need to find the clock. Even if you imagine that it runs on some kind of "intrinsic" clock, it would still need to sync up with time in our universe. For example, if it is a function of total entropy, what mechanism would it use to collect that information?

 

[marcus]

This was an important exchange at post #38 on the previous page.

...
QFT says that vacuum must have some intrinsic energy.
...
IOW: we don't make up some "vacuum energy". Our theories say it's there.

In brief: no. It could have some intrinsic energy, but in most familiar quantum field theories (QED, the Standard Model) the energy is assumed to be zero.

The point is there are VARIOUS interesting ways people study, for how the baseline curvature could arise---they don't all involve vacuum energy. So it's misleading for people to discuss solely in vacuum energy terms, assuming that's the answer, and not bring out the variety.
Here's another example, Chronos gave the link some posts back. You can see it is another NON-VACUUM ENERGY mechanism by which the cosmological constant (baseline curvature) could arise.
http://arxiv.org/abs/1103.4841
Cosmological Constant: A Lesson from Bose-Einstein Condensates
Stefano Finazzi, Stefano Liberati, Lorenzo Sindoni
(Submitted on 24 Mar 2011)
The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.
5 pages, 1 figures

The recent Sakellariadou papers I mentioned in post#41 carry this idea further---that we can TEST proposed QG theory or emergent gravity scenarios by constraints derived from the actual measured value of the curvature constant.

 

[Darryl]

http://www.scilogs.com/the-dark-mat...ience-discussions-on-the-future-of-cosmology/

"The work by David Wiltshire (his lecture notes) and Thomas Buchert already indicates that inhomogeneities could possibly make the Universe appear to an observer situated within such an underdensity as if it's expansion is accelerating, although in truth it is not. That is, the inhomogeneities appear to be of the correct magnitude to eliminate the need for Lambda, Lambda (dark energy) merely being an apparent effect mis-interpreted by the supernova type 1a data."

"Within about 300 Mpc, where we can say that we have the best measurements, the Universe is nicely consistent with MOND. The mass-to-light ratios of galaxy groups are less than 10 (Milgrom 1998 and Milgrom 2002), i.e. there is only baryonic matter. The observationally inferred increased density of baryonic matter at distances larger than 300 Mpc would then perhaps be due to cosmological models being inappropriate, i.e. that the currently used red-shift--distance relation may be wrong."

 

[mfb]

Blog posts are not acceptable references. I know that Pavel Kroupa has publications along that line, however. But keep in mind that this is an extreme minority view. Most of the astrophysicists disagree with his opinion that data would be consistent with such a model.

 

[marcus]

A point that has been clarified in this thread---e.g. think of the John Baez quote in post #41 at the top of this page as a kind of clarifying challenge---is that the choice of how to think of the topic here is NOT A SIMPLE DICHOTOMY. It's not a strict either-or.
What's given is that what we actually measure is the longterm expansion rate which I've called the baseline expansion rate, or baseline curvature of spacetime, but there are several ways to think about this:
1. We can take it as a physical constant and not ask why it is the size it is. The longterm rate being approached as the universe thins out is 1/173 of a percent per million years. Period. That converts by conventional algebra to a spacetime curvature.
2. Or we can study different explanations for the size and different models for how this (effective) physical constant can have arisen. But without prejudice--without assuming that one particular explanation for the effective longterm curvature is right. We have papers by George Ellis and others, by S. Liberati et al, by M. Sakellariadou et al, by Dan Oriti and his co-authors, and many more, that do this. Other names are Saez-Gomez and Sergei Odinstov. Links to some have been given in this thread.
3. Or we can assume that it is somehow obvious that the longterm or baseline expansion rate is caused by a constant vacuum energy density.

That last assumption is what is encouraged when we refer to the baseline curvature as "dark energy". This invokes something which we don't know exists---a mythical energy density, just the right size, present now everywhere and always. But see the John Baez quote in post #44: "In brief: no. It could have some intrinsic energy, but in most familiar quantum field theories (QED, the Standard Model) the energy is assumed to be zero."
The listener is being encouraged to think of QFT vacuum energy as the explanation---but there are a BUNCH of interesting alternatives being studied. IMO we shouldn't prejudice ourselves. The proposed QFT vacuum energy explanation has been around a long time without achieving much success---no calculation of a vacuum energy the right size to fit the observations of expansion rate asymptote.

 

[marcus]

So the title of the thread doesn't do justice to the scope of this research. The challenge implied by
"Dark energy" may be nothing more than baseline curvature suggests too simple a dichotomy. Some further elaboration is needed:
Yes I suppose it could be NOTHING MORE than a simple constant curvature we observe and accept as we to the constants c, and G, essentially without question. This was one of the two alternatives presented in that Baez quote in post#41
Or it could be A GREAT DEAL MORE---a variety of interesting underlying mechanisms have been proposed that explain how the baseline expansion rate---and possibly other effective proportions we accept, have arisen.
That explain its size and how it may have gotten embedded in the universe as an effective constant.

The difference is we don't need to NAME the effective longterm expansion rate in a way that carries a BIAS as to its cause. That gets an unwary listener immediately into the rut of thinking about it in a particular way. and can drag in a lot of associated unnecessary conceptual baggage.

 

[Haelfix]

1. We can take it as a physical constant and not ask why it is the size it is. The longterm rate being approached as the universe thins out is 1/173 of a percent per million years. Period. That converts by conventional algebra to a spacetime curvature.
2. Or we can study different explanations for the size and different models for how this (effective) physical constant can have arisen. But without prejudice--without assuming that one particular explanation for the effective longterm curvature is right. We have papers by George Ellis and others, by S. Liberati et al, by M. Sakellariadou et al, by Dan Oriti and his co-authors, and many more, that do this. Other names are Saez-Gomez and Sergei Odinstov. Links to some have been given in this thread.
3. Or we can assume that it is somehow obvious that the longterm or baseline expansion rate is caused by a constant vacuum energy density.
.

Yes, so as I was hoping to convey 2 and 3 are fine, 1 is completely wrong though. Classically this is how things behave, but one cannot treat it as just a constant when quantum mechanics is involved. It is absolutely not like hbar or c or anything of that nature. Note that this is completely independent of which side of the field equations it is put on. The problem is that quantum operators undergo renormalization. The Ricci tensor and Ricci scalar, now have hats on them, and they will generate an effective cosmological constant under RG flow. Even if you set by hand the parameters to zero at one scale, they will generically reappear at another scale b/c (and this is important) no symmetry principle protects the CC from radiative corrections.. Even if nothing about the assumed physics is associated with the stress energy tensor!

Again, something within the rules of the game has to be altered for this conclusion not to hold and that's why its such a difficult question for physicists. All of the papers that are linked to within this thread implicitly or explicitly changes something drastic within the laws of physics, and that's perfectly fine, but you are looking at very deep principles that require modifications.

 

[Haelfix]

Incidentally, this is an old fashioned debate that has a completely analogous statement within the context of the hierarchy problem. When 'T Hooft brought a lot of physicists attention to finetuning problems within physics it was instantly pointed out by many physicists (Sydney Coleman and others) that for instance in the case of the hierarchy problem who cares if the Higgs mass is some very small number, far from its 'natural' Planckian value, its just a parameter that is set by experiment. There, problem solved, we have a working model that matches experiment!

It took about 3 years of conferences to then convince people that there was more to it than that. The problem really only becomes tangible when you attempt to embed the standard model into another theory with more explanatory power (for instance one that explains the Higgs mass). At that point you now are hit by the full weight of the hierarchy problem, b/c the dangerous hypothetical cancellations now become actual physical cancellations that are completely impossible to explain.

Here again with the CC something like the above is the case (only it's much worse).

 

[marcus]

A point that has been clarified in this thread---e.g. think of the John Baez quote in post #41 at the top of this page as a kind of clarifying challenge---is that the choice of how to think of the topic here is NOT A SIMPLE DICHOTOMY. It's not a strict either-or.
What's given is that what we actually measure is the longterm expansion rate which I've called the baseline expansion rate, or baseline curvature of spacetime, but there are several ways to think about this:
1. We can take it as a physical constant and not ask why it is the size it is. The longterm rate being approached as the universe thins out is 1/173 of a percent per million years. Period. That converts by conventional algebra to a spacetime curvature.
2. Or we can study different explanations for the size and different models for how this (effective) physical constant can have arisen. But without prejudice--without assuming that one particular explanation for the effective longterm curvature is right. We have papers by George Ellis and others, by S. Liberati et al, by M. Sakellariadou et al, by Dan Oriti and his co-authors, and many more, that do this. Other names are Saez-Gomez and Sergei Odinstov. Links to some have been given in this thread.
3. Or we can assume that it is somehow obvious that the longterm or baseline expansion rate is caused by a constant vacuum energy density.

That last assumption is what is encouraged when we refer to the baseline curvature as "dark energy". This invokes something which we don't know exists---a mythical energy density, just the right size, present now everywhere and always. But see the John Baez quote in post #44: "In brief: no. It [the vacuum] could have some intrinsic energy, but in most familiar quantum field theories (QED, the Standard Model) the energy is assumed to be zero."
...

Yes, so as I was hoping to convey 2 and 3 are fine,...

I'm glad you like option 2! I like 2 myself. Once it's clear that what we measures when we measure the cosmological constant is the asymptotic (baseline) expansion rate it is an intriguing and natural question to ask how it arises in our universe, why it is the apparent size it seems to be. Several of the authors mentioned have gotten into ideas of quantum cosmology pre-geometry, at this point. Obviously the spacetime manifold of GR is classical---it is an idealization that doesn't embody quantum mechanics. There must be an underlying quantum pre-geometry that it arises from. And in that process the effective constants governing the classical spacetime may also arise.

We see that kind of thing happening in, for example, the papers by Oriti or by Sakellariadou, and their collaborators.

 

[bbbl67]

I know of no scientific reason to suppose that "dark energy" is anything more than the cosmological curvature constant identified by Einstein in 1917 as occurring naturally in the GR equation for spacetime curvature.

I agree with you, but the curvature of the universe wouldn't make any sense if we didn't compare energy levels, right? Space would be nothing but a flat featureless void, if there wasn't energy in it.

Now, my feeling is that Dark Energy is nothing more than the same thing that led to Big Bang Inflation. Except in the case of Inflation, since the universe was so much smaller that even a slight curvature led to runaway faster-than-light expansion for a brief period of time, until the sphere of Inflation became even bigger and then the observable part of the universe went to a modest sub-lightspeed expansion phase. Basically a super version of the Hubble sphere.