"Dark energy" may be nothing more than baseline curvature

[marcus]

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.

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.

The phrase "dark energy" tends to get newcomers confused because they try to understand something much simpler (a small pervasive constant baseline curvature) in terms of energy. The phrase should probably be replaced by something less misleading.

 

[mfb]

It might eventually turn out to be related to some type of energy. That's possible.

It is purely a matter of interpretation. A constant dark energy density and an explicit cosmological constant lead to exactly the same physics.
If the "constant" is observed to vary with time or space in the future, then a cosmological constant does not work any more.

A different name might have been better, in particular to avoid confusion with dark matter. But we cannot change it here.

 

[fresh_42]

It is purely a matter of interpretation. A constant dark energy density and an explicit cosmological constant lead to exactly the same physics.
If the "constant" is observed to vary with time or space in the future, then a cosmological constant does not work any more.

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

A different name might have been better, in particular to avoid confusion with dark matter. But we cannot change it here.

I like to ask how "dark energy" contributes to the overall balance. I usually read of about 0.75. Is such a notation compatible with the interpretation of curvature which I also like the best since it seems somehow natural? Wouldn't this apply an energy to a geometric object?

 

[Haelfix]

You could in principle play the same game with a time dependent dark energy term. Normally something like quintessence is interpreted as living on the right hand side of the field equations as the varying potential of a scalar field, but nothing stops you from bringing it over to the left hand side and interpreting it as having to do with geometry.

The dynamics are the same, provided Einstein's equations hold exactly, its just a matter of terminology*.

*Bad terminology incidentally, in cosmology the word 'curvature constants' means something very different.

 

[mfb]

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

Well, we wouldn't call it constant then I guess. On the other hand, the Hubble "constant" is not constant in time either.

I like to ask how "dark energy" contributes to the overall balance. I usually read of about 0.75. Is such a notation compatible with the interpretation of curvature which I also like the best since it seems somehow natural? Wouldn't this apply an energy to a geometric object?

The addition to approximately 1 needs an interpretation as energy density or something similar.

 

[timmdeeg]

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.

Two questions:

Do you say that the cosmological constant / dark energy is not vacuum energy? And what would this mean regarding the Friedmann equation?

What means "universe's baseline curvature"?

 

[marcus]

Those questions are pretty well answered in the 2010 article "Why all these prejudices against a constant?" Google the title.

You just write the Friedmann equation with a constant spacetime curvature on the lefthand side (like a constant of integration). It does not involve any matter term on the right hand.

There is no successful calculation correctly predicting a corresponding "vacuum energy". If you want, call the cosmo constant "vacuum curvature" and forget about energy.

The cosmo curvature constant, as a curvature is unavoidable. Einstein introduced it with the Lambda notation, on the lefthand side of GR where it appears naturally as any term would that is allowed by the symmetries of the theory. It had not been proven to be zero so he put it in. Bianchi and Rovelli explain this adequately, I think.
http://arxiv.org/abs/1002.3966
http://inspirehep.net/record/846447?ln=en
https://www.google.com/?gws_rd=ssl#q=Why+all+these+prejudices+against+a+constant

 

[timmdeeg]

Ok, thanks. So, either one has to postulate vacuum energy connected with some understanding of how it curves spacetime or one postulates an ad hoc existing "vacuum curvature" without assuming the cause. Would that be correct?

 

[marcus]

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.

 

[yogi]

The notion of curvature of nothing is based upon Einstein's formulation of space as static. Using Friedmann's equation rho = [q][3H^2/4piG)] and taking q per de Sitter [c^2/R], the dynamic solution for a zero energy universe [(rho)(c^2)/3 = -P] leads to the same result as lambda = G as originally proposed by Einstein. No dark energy needed ...because for the zero energy universe the solution exponential?

 

[marcus]

Hi Yogi, I'll propose a Friedmann equation context you can use or not as you like. In units with c=1, spacetime curvature has units either inverse length squared (inverse area) or inverse TIME squared.
The latter is convenient and it means that Einstein's cosmological curvature constant Λ is the square of a reciprocal time. Same units as H^2 in the Friedmann.

So we can write

H²(t) - Λ/3 = [some constant] ρ(t)

where ρ rho is the energy density including all usual types of matter and energy, so that is how the Hubble rate H(t) evolves.

Eventually ρ → 0 in an expanding universe, as things thin out. So Λ/3 is the limit of the square of H(t) as t→∞

So you can define H_∞ as the limit that H(t) approaches. H_∞² = Λ/3

H²(t) - H_∞² = [some constant] ρ(t)

This gives the cosmo constant some real tangible meaning. Expressed as H_∞, it turns out that H_∞ is about
1/173 percent per million years. that is the asymptotic expansion rate---the present rate H being 1/144 percent per million years.

 

[marcus]

The constant in the Friedmann equation (that I called "some constant" earlier) is either 8πG/3, if you are using c=1 units,

or if you like to include c it is that same thing divided by c², namely 8πG/3c²

This is the spatially flat case of the Friedmann, which is what mostly gets used since the observed spatial curvature is so close to zero.
I hope you like this context for working with the Friedmann equation. It's fairly clean and easy to use. The critical energy density does not involve any "dark energy" component of course. But it includes dark matter---there is pretty good scientific evidence that exists.

The Bianchi Rovelli 2010 paper is really worth studying.
http://arxiv.org/abs/1002.3966
http://inspirehep.net/record/846447?ln=en
https://www.google.com/?gws_rd=ssl#q=Why+all+these+prejudices+against+a+constant
I see Google Scholar says it has been cited 65 times, listed here. Included are some citations in books but most are in research publications
https://scholar.google.com/scholar?...2&um=1&ie=UTF-8&lr&cites=10452416241992441383

 

[timmdeeg]

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.

I've read the Bianchi Rovelli paper and if I understand them correctly they say if the cosmological constant was a "great mystery" then all natural constants are a great mystery. Hard to oppose. And yes, the prediction of QFT is in deed far off. Hopefully I got your (interesting) point.

 

[Haelfix]

Classically, the cosmological constant is just that.. A constant of integration, and indeed it can be anything you want as there is no measure over the real numbers (1.59 is just as likely or unlikely as 1e-120 in natural units). It matters not one wit if you put it on the left hand side or the right hand side, that's just a matter of how you want to group things and it's perfectly well understood and trivial at this level.

The cosmological constant problem is a problem about the quantum field side of this thing, really the effective field theory of gravity at large distances. Note that Rovelli's paper is completely specious on this point, b/c it doesn't even try to address the fundamental problem. And the fundamental problem is that the cosmological constant in the quantum regime apparently takes contributions from ALL physics, everything we know about from the Hubble scale all the way down to the Planck scale. Forget about the Planck scale, the problem is already extreme at the level of things we understand very well for instance the physics from the Hubble scale to the physics of quantum electrodynamics. Already there you have a buildup of quantum field theoretical modes from objects like electrons that we understand well, and clearly something is very wrong with the calculations (more on this in a bit).

Viewed in this light, it cannot and should not be seen as 'just a constant', anymore than the hierarchy problem in particle physics can be seen as just 1 finetuned number. Technically what's going on, is that the cosmological constant is radiatively unstable. So for instance, you might take the point of view of Rovelli and argue that there is identically zero contribution from quantum mechanics (and instead have it just remain perfectly classical). But first problem, you have to show this explicitly, you can't just wave your hand (which is completely circular logic). Second problem, this is backwards (one derives classical mechanics from quantum mechanics, not the other way around) and third problem, if you adjust the physics at one scale to cancel the quantum contributions, you now have to figure out a way or a reason to adjust the same physics to the next scale. This would be like if you had an unexplained problem with the trajectory of baseballs being hit on Alpha Centauri that you wanted to explain, but found out that the answer depended very sensitively on some tiny detail about the unknown physics of the quarks within the ball (except some 15 orders of magnitude worse than that). That sort of scale sensitivity almost never happens in physics absent some symmetry that would force it upon us, so when we see a problem that requires it, it seems unnatural to us.

Now you could just say that this is a calculation error of humans. But this too is wrong, or at least its completely not obvious exactly what's going wrong. You see, the quantum vacuum does produce very real tangible effects. Effects that we have calculated already to quite exquisite precision. For instance in QED the famous Lamb shift is known to 9 or 10 decimal places, and is indeed one of the most accurate and successful predictions ever computed in the history of physics, we know this with much more precision than anything to do with gravity. Now, this same effect, 'gravitates' in atoms b/c it contributes to the total mass and precision tests of the equivalence principle shows that indeed it does (with some ridiculously small error bars). Therefore it naively seems like the effect of quantum mechanics is not identically zero, that they do have some contribution to the value of the CC, at least within the vicinity of atoms.

This of course makes the problem tangibly worse, bc now instead of figuring out a way to make the contributions identically zero for all quantum mechanical processes (like Rovelli would like) we have to figure out a way to make the sum of all such processes (through all scales) ridiculously tiny. This sum of unknown quantities will look schematically something like this 2 - 5 + .4 + .003 - .00002 + .000000000985 + ... = 1 e -120. In other word each number in the term (corresponding to contributions arising from extremely different physical phenomena, many of which are unknown) somehow mysteriously cancels each other number to some incredible accuracy. Why this is the definition of the (new) cosmological constant problem.

 

[timmdeeg]

Thanks, very interesting post!

You see, the quantum vacuum does produce very real tangible effects. Effects that we have calculated already to quite exquisite precision. For instance in QED the famous Lamb shift is known to 9 or 10 decimal places, and is indeed one of the most accurate and successful predictions ever computed in the history of physics, we know this with much more precision than anything to do with gravity. Now, this same effect, 'gravitates' in atoms b/c it contributes to the total mass and precision tests of the equivalence principle shows that indeed it does (with some ridiculously small error bars). Therefore it naively seems like the effect of quantum mechanics is not identically zero, that they do have some contribution to the value of the CC, at least within the vicinity of atoms.

According to R.L. Jaffe "Casimir forces can be computed without taking reference to zero point energies." So, from this one couldn't argue that quantum fluctuations do contribute to the CC. On the contrary the Lamb shift does. And not only that, I wasn't aware of the conclusion that it "gravitates". Very interesting point, which seems to propose that there should be somehow a contribution to the CC. Is there any idea from researchers why that is so tiny?

 

[nikkkom]

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.

Except Occam's razor.

2. you have to make up some "vacuum energy" that bends the spacetime just the right observed amount.

QFT says that vacuum must have some intrinsic energy.

You are right saying that currently we can't calculate it (calculations are divergent, and even with an energy cutoff they give insane huge values), but it exists, and hopefully one day we will be able to calculate it correctly. It's rather unlikely to turn out to be zero.

IOW: we don't make up some "vacuum energy". Our theories say it's there.

 

[nikkkom]

According to R.L. Jaffe "Casimir forces can be computed without taking reference to zero point energies."

And many other things do not depend on zero point energy - as long as you are using Special Relativity framework. But when you use General Relativity...

And not only that, I wasn't aware of the conclusion that it "gravitates". Very interesting point, which seems to propose that there should be somehow a contribution to the CC. Is there any idea from researchers why that is so tiny?

...things change. GR's stress-energy tensor places energy into its T00 element, not its difference from "zero point". Thus, if zero point energy is nonzero, then stress-energy tensor of empty space is nonzero too. It gravitates.

 

[timmdeeg]

GR's stress-energy tensor places energy into its T00 element, not its difference from "zero point". Thus, if zero point energy is nonzero, then stress-energy tensor of empty space is nonzero too. It gravitates.

I think if the CC acts like a vacuum energy density, it would exert negative pressure, represented by the components ##T##ⁱⁱ.

 

[Haelfix]

According to R.L. Jaffe "Casimir forces can be computed without taking reference to zero point energies." So, from this one couldn't argue that quantum fluctuations do contribute to the CC. On the contrary the Lamb shift does. And not only that, I wasn't aware of the conclusion that it "gravitates". Very interesting point, which seems to propose that there should be somehow a contribution to the CC. Is there any idea from researchers why that is so tiny?

Right, so there are definitely subtleties regarding what is or is not vacuum energy, or really what you call it. This is why people frequently pick a weakly coupled, Abelian theory to make the point where we have, to a great approximation, the ability to talk about things like vacuum polarization, mass renormalization and the nontrivial structure of the zero point energy of electrons and where we don't get into too many messy technicalities of quantum field theory. For instance, the case is in principle much stronger for QCD. The mass of the quarks is only a small fraction of the mass of the nucleus, therefore almost all of the mass of things we see around us arises from quantum effects eg the gluon kinetic and potential energies that are constantly fluctuating in the QCD vacuum. Clearly we don't need to worry about violating the equivalence principle in that case, but there of course the analysis is less clean b/c of the subtleties that Jaffe mentions and for other reasons (confinement etc). In any event, equivalence principle tests in the case of platinum and Aluminum atoms shows that the Lamb effect (in those atoms) satisfies the equivalence principle to one part in 10 ^6, which shows that at the very least something is going on.

Anyway whatever 'it' is, clearly gravitates, and so part of a solution (if you want to explain it away) would be to precisely explain why those effective field theory arguments are wrong (which amounts to essentially rewriting large parts of quantum field theory and/or General relativity). Or if they are right, how do these effects cancel with each other to such fantastic accuracy? So you see, it is a very big and difficult problem no matter how you slice it.

As for potential ideas for why it is tiny.. Again, many many ideas. All of which have many, many problems. There are many review articles out there, for instance (where you can see the arguments I gave flushed out in a little more detail):
http://arxiv.org/abs/hep-th/0603249
http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.61.1
or a recent one
http://arxiv.org/abs/1502.05296

 

[Haelfix]

I think if the CC acts like a vacuum energy density, it would exert negative pressure, represented by the components ##T##ⁱⁱ.

The CC term enters Einsteins equation with the metric tensor Guv. So you have something like Rhovac Guv (where I am forgetting factors of 8pi and G), so it will enter in along the diagonal matrix elements of the stress energy tensor.

 

[timmdeeg]

Haelfix, thanks for your valuable explanations.
You mentioned this paper, http://arxiv.org/abs/1502.05296 , wherein Padilla referring to quantum fluctuations states that "the finite contributions ... are cancelling to at least of one part in 10⁶⁰ in Nature." Such fine tuning seems weird and obviously not at all understood. So, in principle one could question whether it is less weird to not neglect the existence of gravitating quantum fluctuations, but to prefer the idea of perfect cancellation due to an yet unknown physical background (e.g. quantum gravity) and hence to think of the CC as a natural constant as proposed by Bianchi and Rovelli. Is it a matter of personal taste?

 

[Haelfix]

Haelfix, thanks for your valuable explanations.
You mentioned this paper, http://arxiv.org/abs/1502.05296 , wherein Padilla referring to quantum fluctuations states that "the finite contributions ... are cancelling to at least of one part in 10⁶⁰ in Nature." Such fine tuning seems weird and obviously not at all understood. So, in principle one could question whether it is less weird to not neglect the existence of gravitating quantum fluctuations, but to prefer the idea of perfect cancellation due to an yet unknown physical background (e.g. quantum gravity) and hence to think of the CC as a natural constant as proposed by Bianchi and Rovelli. Is it a matter of personal taste?

How you decide to cancel things is up to the theorist. You can try to 'degravitate' the quantum vacuum (thus solving the 'old' cosmological constant problem), such that each individual contribution is zero.. Many ideas like this, for instance, straight modifications of general relativity like Unimodular gravity and ideas like DGP gravity. You can try to 'adjust' the value of each subsequent piece of new physics so that there are approximate cancellations. You can look for a symmetry to explain things (like supersymmetry or conformal symmetries).

The problem somehow seems more general than just having quantum gravity save you though. The problem as I said seems to be most well posed at extremely long distances, in well understood regimes of physics far from the high energy frontier. Why on Earth would high energy physics know about Hubble scale phenomenon to such precision.

Mathematically you can restate the problem as follows: There are two length scales in this problem. The infrared cutoff scale (taken for instance to be the Hubble scale) and the ultraviolet length scale (which we can choose to be the Planck scale). A quantum field theory calculation (that works in almost all other sectors of physics) predicts that the vacuum energy would gravitate to something approximately proportional to the ultraviolet cutoff to the 4th power. This can't be right, bc experiment says that the vacuum gravitates like something roughly proportional to the infrared cutoff scale to the 1st power. Your job is to invent a mechanism or a new theory that gives this result.

 

[Chronos]

Why should it be anyone's job to invent a new theory based on numerology. The Egyptians did that about 4000 years ago -.it's now called astrology.

 

[Haelfix]

Sorry but that is nonsense, the cosmological constant problem is not numerology. There is a number that is fixed by experiment, and two central pillars of theoretical physics that together outputs a wrong value and prediction. It is a theorists job to explain this discrepancy. The solution of the problem requires either a mechanism that produces the correct value, as well as an explanation about what is going wrong, or a new theory.

 

[marcus]

... contribution is zero.. Many ideas like this, for instance, straight modifications of general relativity like Unimodular gravity...

Interesting. Let's sample current activity and research interest in Unimodular (a variant of GR that gives essentially the same observable results but where the constant vacuum energy would not affect curvature so vacuum energy would be irrelevant to cosmo const i.e. to baseline expansion rate)
Let's sample papers from Jan 2014 to present:
http://arxiv.org/find/grp_physics/1/ti:+AND+unimodular+gravity/0/1/0/all/0/1

37 come up. Here are the first 16:
1. arXiv:1602.04771 [pdf, ps, other]
Generalizing unimodular gravity
Diego Saez-Gomez (IA, U. of Lisbon)
Comments: 8 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
2. arXiv:1602.03172 [pdf, ps, other]
Unimodular f(T) gravity
S. B. Nassur, C. Ainamon, M. J. S. Houndjo, J. Tossa
Comments: 11 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
3. arXiv:1601.04112 [pdf, ps, other]
The bounce universe history from unimodular F(R) gravity
S. Nojiri, S.D. Odintsov, V.K. Oikonomou
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th)
4. arXiv:1512.07223 [pdf, ps, other]
Unimodular F(R) Gravity
S. Nojiri, S.D. Odintsov, V.K. Oikonomou
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th)
5. arXiv:1511.08517 [pdf, other]
The KLT relations in unimodular gravity
Daniel J Burger, George F. R. Ellis, Jeff Murugan, Amanda Weltman
Comments: 28 pages, 2 figures
Subjects: High Energy Physics - Theory (hep-th)
6. arXiv:1511.06560 [pdf, ps, other]
Essential nature of Newton's constant in unimodular gravity
Dario Benedetti
Comments: 15 pages
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
7. arXiv:1511.01805 [pdf, ps, other]
Cosmological perturbation of Unimodular Gravity and General Relativity are identical
Abhishek Basak, Ophélia Fabre, S. Shankaranarayanan
Comments: 24 pages, no figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph)
8. arXiv:1510.00188 [pdf, ps, other]
BRST symmetry of Unimodular Gravity
S. Upadhyay, M. Oksanen, R. Bufalo
Comments: 29 pages
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
9. arXiv:1506.07410 [pdf, other]
First Order formulation of Unimodular Gravity
Enrique Álvarez, Sergio González-Martín
Comments: 4 pages
Journal-ref: Phys. Rev. D 92, 024036 (2015)
Subjects: High Energy Physics - Theory (hep-th)
10. arXiv:1505.04978 [pdf, ps, other]
How unimodular gravity theories differ from general relativity at quantum level
R. Bufalo, M. Oksanen, A. Tureanu
Comments: 35 pages; v4: included a full treatment of nonlocally linearly dependent generators as Appendix A, Refs. 28 and 29 added, extended the discussion on physical degrees of freedom, boundary terms, and conclusions
Journal-ref: Eur. Phys. J. C 75 (2015) 477
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
11. arXiv:1505.01995 [pdf, other]
Quantum Corrections to Unimodular Gravity
Enrique Álvarez, Sergio González-Martín, Mario Herrero-Valea, Carmelo P. Martín
Comments: 34 pages
Subjects: High Energy Physics - Theory (hep-th)
12. arXiv:1505.00022 [pdf, ps, other]
Unimodular Gravity Redux
E. Álvarez, S. González-Martín, M. Herrero-Valea, C. P. Martín
Comments: 4 pages
Journal-ref: Phys. Rev. D 92, 061502 (2015)
Subjects: High Energy Physics - Theory (hep-th)
13. arXiv:1501.05848 [pdf, other]
The Renormalization Group flow of unimodular f(R) gravity
Astrid Eichhorn
Comments: 17 pages, 2 figures; new version with some clarifications, identical to version to appear in JHEP
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
14. arXiv:1412.6205 [pdf, ps, other]
Unimodular Theory of Gravity and Inflation
Inyong Cho, Naveen K. Singh
Comments: 11 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
15. arXiv:1410.6163 [pdf, ps, other]
On the UV structure of quantum unimodular gravity
Ippocratis D. Saltas
Comments: 11 pages plus Appendix; Some clarifying comments added, results unchanged; Version to appear in Physical Review D
Journal-ref: Phys. Rev. D 90, 124052 (2014)
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
16. arXiv:1409.8014 [pdf, ps, other]
Canonical Analysis of Unimodular Gravity
J. Kluson
Comments: 11 pages, v2 references added
Subjects: High Energy Physics - Theory (hep-th)

reference [10] of Buffalo et al (which shows up on page 2 a couple of times) is to the PADILLA paper.
there seem to be ways to avoid Padilla's objections---different versions of unimodular. Anyway interest is persistent and lively Padilla notwithstanding.

Padilla has is OWN RIVAL variant of gr ("fab four") according to which vacuum energy would not "gravitate" ie. would not contribute to curvature, so he may be a bit overly dismissive of the various unimodular options that you see in the above list of research titles.

 

[marcus]

the first one on that list is fascinating!
http://arxiv.org/abs/1602.04771
Generalizing unimodular gravity
Diego Saez-Gomez (IA, U. of Lisbon)
(Submitted on 15 Feb 2016)
The so-called unimodular version of General Relativity is revisited, which assumes the trace-free part of the equations instead of the usual Einstein equations, what leads naturally to a cosmological constant that may compensate the large value of quantum fluctuations. Here we extend such formalism to some extensions of General Relativity that have drawn a lot of attention over the last years, as f(R) gravity (or its equivalent scalar-tensor picture) and Gauss-Bonnet gravity. The corresponding unimodular version of such theories is constructed. From the classical point of view, the unimodular versions of such extensions are completely equivalent to their originals, but an effective cosmological constant arises naturally, what may provide a richer description of the universe evolution. Moreover, conformal transformations within unimodular gravities lead to some corrections that may affect their solutions. Here we analyze the case of Starobinsky inflation and compared with the original one.
8 pages

Saez-Gomez references [2] and [7] are to Padilla (and his critique) and they come up already on page 1.

 

[Chronos]

Another paper that might be worth a look is http://arxiv.org/abs/1103.4841, Cosmological Constant: A Lesson from Bose-Einstein Condensates.

 

[marcus]

Nice! Thanks, Chronos. Another angle on the CC as a feature of condensate (geometry as condensate this time) is in
[66] Gielen S., Oriti D., Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics, New J. Phys. 16 (2014), 123004, arXiv:1407.8167.

This is reference [66] of the valuable recent review article by Gielen and Sindoni:
http://arxiv.org/abs/1602.08104
Quantum cosmology from group field theory condensates: a review
Steffen Gielen, Lorenzo Sindoni
(Submitted on 25 Feb 2016)
We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate" of a large number of quanta of geometry which are given by excitations of the GFT field over a "no-space" vacuum. We emphasise conceptual foundations, relations to other research programmes in GFT and the wider context of loop quantum gravity (LQG), and connections to the quantum physics of real Bose-Einstein condensates. We show how to extract an effective dynamics for GFT condensates from the microscopic GFT physics, and how to compare it with predictions of more conventional quantum cosmology models, in particular loop quantum cosmology (LQC). No detailed familiarity with the GFT formalism is assumed.
46 pages, 5 figures, invited review for SIGMA Special Issue on Tensor Models, Formalism and Applications

==quote http://arxiv.org/pdf/1602.08104.pdf page 39==
In the second approach, one tries to interpret corrections to an effective Friedmann equation (arising, for instance, from different types of GFT interactions) as matter fields or as an effective cosmological constant. This possibility was outlined in [66] where we point for further reference. It is potentially very interesting, as it may, for example, raise a hope to solve the cosmological constant problem through GFT condensates, but has not been explored much so far.
==endquote==

 

[marcus]

Chronos, George Ellis, whom we know as a grand old man of GR and Cosmology, has an interesting paper with some others where they look at how we will eventually be able to distinguish between Unimodular Gravity (UG) and standard GR, by observation of quantum effects. GR and UG are expected to be equivalent at the classical level, same predictions, as they point out.

arXiv:1511.08517 [pdf, other]
The KLT relations in unimodular gravity
Daniel J Burger, George F. R. Ellis, Jeff Murugan, Amanda Weltman
(Submitted on 26 Nov 2015)
With this article, we initiate a systematic study of some of the symmetry properties of unimodular gravity, building on much of the known structure of general relativity, and utilising the powerful technology developed in that context. In particular, we show, up to four-points and tree-level, that the KLT relations of perturbative gravity hold for tracefree or unimodular gravity.
28 pages, 2 figures

==quote from page 3==
...While it does not resolve the issue of the cosmological constant, UG does relegate it to an integration constant to be fixed by empirical data. It does so by decoupling fluctuations of the quantum vacuum from gravitational physics rendering an entirely viable classical theory of gravity [9]. In fact, at the classical level, UG is expected to be completely indistinguishable from GR [10, 11] (see also the extended discussion in [12]) even though the former only preserves a Weyl transverse subgroup, WTDiff(M) of the full Diff(M) symmetry group of GR. This difference will, however, manifest at the quantum level. With an ultimate goal of exploring the quantum differences between unimodular gravity and GR in mind, it is certainly important to understand the extent of their similarities...
==endquote==

I think this is a major paper, also several the authors' track records deserve note e.g.
http://inspirehep.net/author/profile/A.Weltman.1
http://inspirehep.net/author/profile/J.Murugan.1

==excerpt from page 20==
...Consequently, unimodular gravity, the truncation of the Einstein gravity to its tracefree degrees of freedom, also exhibits the same rich structure as GR does, at least with respect to its (tree-level) relationship to gauge theory via the KLT relations. This is to be expected since, classically the two theories are equivalent, and the tree-level amplitudes only encode the semi-classical interactions of the gravitons.

General relativity and unimodular gravity are however expected to differ at the quantum level [10], so the study of graviton scattering is key to breaking the degeneracy. To this end, what is required are the 1-loop and higher amplitudes. This is a formidable task indeed in the context of standard Feynman diagram computations. However, the technological renaissance in amplitude calculations in recent years has seen the development of powerful unitarity methods (see [4] and references therein) that use precisely the KLT relations to obtain loop amplitudes from trees. It would be of immense interest to extend our tree-level results to higher loops. Then there is the issue of coupling to matter. One of the key phenomenological motivations for UG is the fact that, unlike in GR, gravity no longer couples to matter potentials [17]. This necessarily means that graviton-matter scattering should differ in the two theories. Again, amplitude technology and the KLT relations in particular allow for such scattering amplitudes to be computed (at least in some restricted cases) [18]. We would be curious how these amplitudes change in unimodular gravity.

In any event, part of the motivation for this work was to expose these powerful field theoretic methods to a broader community and we hope that, if nothing else, we have succeeded in elucidating further the wonderful legacy left to us by Einstein 100 years ago.
==endquote==

 

[Chronos]

Another, interesting discussion is offered by this heavily cited paper: http://arxiv.org/refs/1205.3365,Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask). Given I have only a drive-by familiarity witht unimodular gravity, I need to study the papers you cited. It's on my do list

 

[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.