How Are We to Make Progress With w?

By Mark Trodden | August 2, 2005 7:31 am

Oops, there I go again with the provocative “w” in my title. Once again, I feel compelled to tell you up front that this post is about dark energy, not “dubya”.

One of my primary research interests over the past six or seven years has been the question of what is driving the accelerated expansion of the universe. As I’ve mentioned before, cosmologists now have a clear and surprising accounting of the energy budget of the cosmos. Multiple techniques provide compelling evidence for (roughly) 5% baryonic matter (the stuff of which you are made, that makes up planets and stars, and which occupies much of the space between them), 25% dark matter (a mysterious, weakly interacting component that clumps together and provides the immense gravitational wells into which regular matter can form and combine with dark matter to make galaxies) and a whopping 70% dark energy, with negative pressure, sufficiently negative to cause the expansion of the universe to accelerate.

The best-known evidence for this comes from two sources. The first is from observations of the light curves of Type Ia supernovae. These data are much better fit by a universe dominated by a some kind of dark energy than by a flat matter-dominated model. The second is from studies of the small anisotropies in the Cosmic Microwave Background Radiation (CMB), culminating in those made by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The statistical details of these fluctuations allow the extraction of a variety of cosmological parameters, including the relative densities of various cosmic energy components.

As I described in a previous post, it is sometimes convenient to parameterize dark energy by what is called the equation of state parameter, w. This parameter tells us how, if we treat dark energy as a perfect fluid, the pressure is related to the energy density of the fluid. Current observational bounds place w in the range (very roughly) -0.8 to -1.2. Acceleration will occur for any w<-1/3.

Last time I posted on dark energy, I described some of the theoretical challenges raised by the w<-1 region of the observationally allowed range. Here though, I would like to raise the issue of the experimental and observational challenges to making progress on the critical, but difficult question of what is responsible for cosmic acceleration.

Theoretically, there are three broad classes of ideas about the nature of dark energy. The first is that cosmic acceleration may be due to a pure cosmological constant. The second assumes that the true vacuum energy of the universe vanishes, and that the dynamics of some exotic matter component, such as a scalar field, might be driving acceleration. This approach is like having a version of cosmic inflation happen in the late universe, and goes by the name quintessence. The final approach is again to set the vacuum energy to zero, and then to have a long-range modification of General Relativity be responsible for cosmic acceleration.

Which of these sets of ideas (if any) is correct can only be decided through increasingly accurate measurements of our universe and of the microphysical and macrophysical interactions that govern its behavior and evolution. And this is where the big question comes in. What are the best hopes for making significant observational and/or experimental progress in understanding cosmic acceleration? How do we best figure out if w is constant in space and time (a cosmological constant) or not (some kind of quintessence or modified gravity model)? If we manage this, how do we then make further progress towards narrowing down the possibilities and identifying the root of cosmic acceleration?

The great news here is that we are not without ideas (“we” here is not meant to imply that I could build a modern experiment even if my life depended on it). On the “Outer Space” side of all this, there are plans for a number of space and ground based experiments to probe the dark energy through more accurate measurements of supernovae, through even better measurements of the CMB, and through detailed observations of the statistics of gravitational lensing. These are powerful techniques and hold great promise.

On the “Inner Space” side, we will soon see the turn on of the Large Hadron Collider (LHC) at CERN, near Geneva. The world’s biggest machine and particle smasher is expected to reveal new physics at previously inaccessible energies and, perhaps in conjunction with a future International Linear Collider (ILC), may reveal to us a new picture of how particle physics fits together with the physics of space and time. This connection may take the form of supersymmetry (SUSY) or extra spatial dimensions, but we won’t know until we’ve done the experiments. It may be that the new physics discovered at these machines will provide us with a crucial new insight into dark energy.

I’ve been deliberately sparse and sketchy in the last two paragraphs, mentioning only a few types of experiments and techniques. This is because I don’t want to talk about too many experiments or their specifics, or my views of them right here. Rather, I would like to open up a discussion of the best ways of getting at the physics of cosmic acceleration.

Given what we have established about the accelerating universe, what are the most promising ways of making progress? What are the pros and cons of existing and newly proposed ideas? Are there creative ways to get at the microphysical properties of dark energy? I’d love to hear some smart, thoughtful discussion of these issues, of the sort for which Cosmic Variance commenters are becoming known.

  • Sean

    Figuring out why the universe is accelerating just doesn’t push people’s buttons the way that string theory does. (Maybe someone should start a separate blog, “Not Even Lambda.”) If you want a lot of comments, you should write a post titled “The Anthropic Principle R00LZ!” Actually, maybe I’ll do that.

    My guess is that it’s probably a cosmological constant, and that its value is not chosen anthropically, but rather through some formula we haven’t yet discovered. In other words, the same scenario that most physicists would bet on. Measuring w is obviously crucially important, as everything changes if it’s not -1. If it is a cosmological constant, I’m betting we learn the most about it by doing collider experiments and finding out about supersymmetry or whatever else is making typical particle-physics scales so much lower than the Planck scale.

  • Mark

    Interesting bet. I’m never sure why you make the guess that you do though. I’m not particularly interested in a lot of comments here. Rather I was hoping for some of the quality of (many of) those in the strings post.

    Any comments on the promise of observations?

  • Doug


    While, identifying out “best hopes for making significant observational and/or experimental progress in understanding of cosmic acceleration,” is vitally important, as long as we interpret the data in terms of our current theoretical understanding, which now gives us “three broad classes of ideas about the nature of dark energy,” we may not be able to escape this predicament, no matter how accurate the data.

    The real value of the new discovery may be in the message that our fundamental assumptions have to be reexamined. Assumptions that bear on all the issues together that are listed by Smolin in his new paper:

    1) Quantum gravity
    2) Unification
    3) Origin of constants
    4) Meaning of galaxy rotation and recession observations
    5) Foundations of quantum mechanics

    Smolin’s point that these issues remain unresolved “despite decades of determined effort by thousands of extremely talented people,” is the urgent issue confronting modern physics, and a clear understanding of “w” may not be possible to attain until progress is made in finding the errors in our fundamental assumptions, which, as these issues indicate, are bedeviling us.

    Smolin only uses his criticism of string theory in order to focus on the deeper issues of “a much older debate, which has been central to thinking about the nature of space and time going back to the beginning of physics.” While he concentrates on the old “debate between relational and absolute theories of space and time,” the fact is our fundamental assumptions that the universe consists of matter contained by space and time go beyond even that debate.

    One of the most compelling arguments that Smolin uses to assert that a successful fundamental theory must be a background-independent theory is “that the apparent lack of predictability emerging from studies of the string theory landscape is a symptom of relying on background dependent methodologies in a regime where they cannot offer sensible answers.” If our assumption that elemental matter is an indivisible point particle, leads us to intractable difficulties, but changing this assumption to regard matter as ultimately the motion of a string, leads us to nonsensical answers, then perhaps we should question the really fundamental assumption that matter is separate and apart from space and time.

    Some are contending that this assumption lies at the heart of the difficulty. Assuming that matter is composed of nothing but space and time, the reciprocal aspects of motion, is not far removed from the assumption that it is composed of moving strings. It is the modes of motion that are significant in string theory, not the string itself, so a background-free formulation of string theory, which Smolin and many, many others recognize as indispensable, means finding a background-free definition of motion.

    However, this idea is not only revolutionary, it is iconoclastic, because our most fundamental laws are formulated in terms of forces, and our most fundamental theories in terms of energy, all of which ultimately depend upon our definition of motion in a coordinate system of space and time. What could be more wrenching than contemplating the change in the basis of that program?

    Yet, it is becoming clear that this is exactly what is needed. However, a close look at our efforts so far shows a clear reluctance to completely depart from the old paradigm. For instance, in Causal Set theory, we try to start with a background-free set of events and form a metrical background from it! According to Smolin, the background-free view is:

    1) There is no background.
    2) The fundamental properties of the elementary entities (whatever they are) consist ENTIRELY in relationships between them.
    3) The relationships are not fixed, but evolve according to law.

    If we assume that space and time are the only elementary entities that exist, but that they exist not as a background for matter and events, but only as the reciprocal aspects of motion, then we start with no background and a fundamental relationship between these two entities that entirely determines the properties of the system. Of course this requires that a basic progression of space accompany the basic progression of time in constituting the fundamental motion of this system, but we can easily justify this assumption, since we are now able to observe the progression of both in nature.

    The strength of this approach is found in the discretization of the elementary motion of the system; that is, we can easily quantize units of motion without running into the intractable problems of point particles, or the confusion of background dependence inherent in strings.

  • Mark

    Hi Doug, I appreciate the points you make about a quantum theory of gravity, but see them as somewhat apart from the central question here. It is certainly true that the ultimate answer of what is causing the acceleration of the universe may not fall into one of the three classes I mentioned. In fact I commented to that effect.

    However, my post is really about what observations we can carry out to figure out whether w is constant or not, or whether it is -1 or not and what experiments we can do to figure out the microphysical nature of what is leading to acceleration. I see this as somewhat separate from theoretical progress on quantum gravity, which certainly is also needed.

    By the by, I wouldn’t agree that “our most fundamental laws are formulated in terms of forces, and our most fundamental theories in terms of energy”. I’d say our most fundamental theories are formulated in terms of symmetries (general covariance; gauge symmetries). Force laws come out later.

  • Gordon Chalmers

    Anybody care to comment that the quoted value of the cosmological constant is

    Lambda^4 (Lambda/m_{pl})^4.

    This is with Lambdasim 2 TeV. The same value of Lambda roughtly fits the observed pattern of fermion masses.

  • Mark

    Hi Gordon. This has, of course, been noted before. Unless there’s a sensible theory predicting the relationship, it remains numerology for now I’d say.

  • Gordon Chalmers

    It seems that numerology points to instantons or TeV macroscopic black hole supersymmetry breaking (as in the one in our galaxy).

  • Mark

    I’m unaware of these papers. I don’t actually know what the latter means. What does it mean to have TeV macroscopic black hole SUSY breaking? Doesn’t experiment tell us that superpartners, if they exist, have to be at the TeV scale at least, and that SUSY must therefore be broken at that scale (at least for SUSY breaking models I’ve seen)?

  • Arun

    It seems almost anthropic that the 25% clumpy dark matter all lives in the galactic halo, and not in the galactic disk where we live.

  • Doug

    Mark wrote:

    my post is really about what observations we can carry out to figure out whether w is constant or not, or whether it is -1 or not and what experiments we can do to figure out the microphysical nature of what is leading to acceleration.

    I know, but the trouble is that theory interacts with experiment in subtle ways. For instance, the observation of the CMB is assumed to take place in the context of GR cosmology and the big bang. Therefore, the flat geometry that it indicates is perceived to be the result of the energy density of the cosmos, which in turn is used as evidence for dark energy in making up the energy density deficit created by GR in the face of the CMB!

    But what if the observed Euclidean geometry of the cosmos has nothing to do with curvature of spacetime? How accurately we measure it then becomes moot. Nevertheless, I understand your point. Let me make a few suggestions along that line to make up for getting off-topic.

    Since w opposes gravity, it seems that the way to measure it is in connection with gravity. Could it be that it has something to do with the anomalous rotation speeds of stars in the galaxies? In a gravitational system of stars, there must be a gravitational limit at some point beyond which w is more influential than gravity, which, if so, would cause it to act as a potential barrier between star systems, normally keeping them separated individually, but permitting them to associate together collectively. What would be the effect of this condition on the rotational speed of outlying stars in the galaxy? Wouldn’t it tend to add rigidity to the system that might account for the observed speeds? If so, careful analysis should reveal the component attributable to w.

    Another possibility is to look for evidence of the value of w by studying the forces of solid cohesion in matter. It is possible that w becomes positive and gravity becomes negative at the atomic level, which would be the inverse of the gravitational limit referred to above. In this close-range interaction, the forces would be much stronger and would not be self-reinforcing, as in the outer limit, but would be mutually restoring, forming a bond instead of a potential barrier. Since the value of gravity is known, then an analysis of the equilibrium distances in molecular bonds should yield the value of w if the nature of such an interaction were understood.

    However, just as the first suggestion requires laying aside the assumption of the existence of dark matter, as an explanation of the galactic rotational anomalies and the conviction that this explanation is essential for the observed flat geometry in the CMB, this second suggestion requires laying aside the Coulomb force / covalent bond explanation of solid state quantum theory, but the likelihood of phenomenologists going against established theories in their searches like this is slim indeed. Hence, my previous comment.

    As far as the characterization of our fundamental theories as formulated in terms of the laws of force and the equations of energy, I was referring to the laws of Newton and the use of Lagrangians and Hamiltonians, but I wouldn’t argue with the modern interpretation of symmetries lying at the foundation of everything. It’s just that a coordinate system, or background of space and time, is necessary in any case. The point is that a background-free theory of motion will require a definition of motion independent of the structure upon which current theory is founded, and the search for the value of w is constrained by that fact.

  • Gordon Chalmers


    Supersymmetry breaking with black-holes seems to be a bit generic, depending on their structure. Various scenarios can be achieved.

  • Mark

    Gordon. Can you give references to the papers. I still don’t understand how this is supposed to achieve the required fermi-bose mass splittings while keeping the induced cosmological constant small compared to a TeV.

  • Gordon Chalmers

    I suppose that I will have to write more of my unpublished notes which are kept for a few years on this topic, or contact you through email.

  • Gordon Chalmers

    Please try: Gordon Chalmers, hep-th/0209072, but keep in mind that both this is not a model of the entire universe and that there are gauge instantons without the modding. this work is old by my standards. Also, try hep-th/0103255, although there are more details on this work, especially with non-perturbative effects like instantons.

  • Simon DeDeo

    We took a vote in the department here. The faculty (those who showed up for afternoon tea, at least) went heavily in favour of a cosmological constant, the grad students were split on CC versus dark energy, and the undergraduates voted in favour of Omega_m=1 (but I think they were just trying to annoy us.) There were very few votes in favour of “modified gravity”, interestingly, perhaps because many people associate it with phenomenological MOND-like effects, and not so much with extra dimensions and all the hip new string theory.

    I am hoping w

  • Simon DeDeo

    It seems the “less than” sign interferes with the HTML!

    In any case, I am hoping for a w less than negative one, because it would be so insane (and I wrote a paper on it.) Another important thing is to look for a dark energy sound speed. Something other than c^2=1/3 (scalar field) or c=infinity (CC) would be worthy of a Nobel prize for the lucky group (I don’t think it is possible, because of cosmic variance, to distinguish 1/3 from infinity, though — just my guess.)

    In a few years we’ll have lensing data and galaxy counts and so on with sufficient signal to noise that we can compare the linear growth rate of structure with the geometric measurements of expansion from supernovae. That will be an interesting time! Mustafa, Amol and David here have written a paper talking about this sort of thing (astro-ph/0507184), but they don’t consider varying sound speeds — they’re interested in testing DGP.

  • Simon DeDeo

    Oh — and just to add my favourite bit of numerology, the neutrinos are just becoming non-relativistic at the time when the dark energy is coming to dominate.

    Of course, numerology is competitive, so there’s the see-saw mechanism which completes the circle of guess.

  • subodh

    To latch onto a point made by Doug concerning the inherent model dependence of our observations: I have heard (as an audience question in a russian accent in one of one Sean Carrol’s talks on this subject, given at KITP in late 2003– ) that it is also possible to explain away the observed acceleration of the universe were we to drop homogeneity as an assumption in our models, and assume that we live in a ‘locally underdense’ bubble of our universe (and of course using only GR).

    Not that I believe that we actually do live in the center of the universe, but it just shows how we have to be aware. I personally don’t have the expertise to deconstruct experimental data with a critical eye, but thats my problem…

    Latching on to Mark’s thoughts on what if w were exactly -1, and why supposed the particle physics origins of the cosmological constant are so miniscule, has anyone read this article by R.L.Jaffe: hep-th/0503158? In it, Jaffe argues that the Casimir energy might have nothing to do with ‘zero point’ energies, hence calling into question the supposed reality of zero point energies (recalling that people have often taken the existence of the Casimir force as proof of the realness of zero point energies, hence the fact that particle physics has to account for itself in terms of the cosmological constant it generates)… food for thought i guess…

  • Sean

    Subodh — If I recall correctly, that Russian voice belonged to Andrei Linde. See his paper Do We Live in the Center of the World? Even he doesn’t think it’s likely, but it’s a possibility. (I almost wrote “logical possibility”, but that might be too strong.)

    I don’t think that Bob Jaffe’s paper really calls into question the existence of zero-point energies; it just shows that the Casimir effect between two plates disappears as you make the plates non-conducting. The Casimir effect really is evidence for the existence of vacuum fluctuations, but then again so is the Lamb shift or the running of the QCD coupling. Of course, the Casimir effect has never said anything about the gravitational effect of zero-point energies, which underlies the cosmological constant problem.

  • Jill

    I’m no expert, but I’m betting that w will turn out to be less than -1. Why? Because whenever theorists declare something to be implausible, it turns out to be true. Note that this principle would have allowed me to predict the discovery of cosmic acceleration….

  • Jill

    Simon Said: “In any case, I am hoping for a w less than negative one, because it would be so insane (and I wrote a paper on it.) Another important thing is to look for a dark energy sound speed. Something other than c^2=1/3 (scalar field)”

    Is that correct? I thought perturbations propagate at c in a scalar field [with canonical kinetic term]?

  • Sean

    Jill, there is a large number of things that theorists declare to be implausible, which later turn out to be true. Still, I would bet that it’s much smaller than the number of things that theorists declare to be implausible and turn out to be false. It’s true that you would have gotten the acceleration of the universe correct, but you may also have bet that the universe was not spatially flat, and that the dark matter was made of chocolate truffles.

    Joking aside, the fact that we were all surprised about the acceleration is one of the reasons people take ideas like quintessence, phantom energy, and modified gravity at all seriously. None of these is theoretically compelling, but we’ve (hopefully) learned to keep an open mind.

  • Simon DeDeo

    Hi Jill — yes, my bad. c^2=1 for a scalar field, not 1/3.

  • Clifford

    Mmmmmm, chocolate. -cvj

  • Jill

    Sean….point taken. :-) Though I think live octopus tentacles is a more plausible hypothesis than truffles. I still hope that w will turn out to be less than – 1 because I think that will lead to faster progress. Nothing like a good kick in the pants to get the brain working, eh?

    To get back to Mark’s question—my wild guess is that we would get a better understanding of what w should be if we could work out what the hell is going on here:

    I say that because my guess is that to understand dark energy we will need a better understanding of the global structure of space time. You know, if the Universe has some weird shape [as in the recent Land/Magueijo stuff] that has got to tell us something big. OK, I’m just parroting what my boss said, but he sure made it sound convincing….

  • Risa

    So, there will be lots of great constraints from the next generation of astrophysical dark energy experiments on the horizon — combining galaxy clustering, cluster evolution and weak lensing with supernovae data should give us better than a few percent constraint on w in the next 5 years. But if our results are consistent with w=-1, will we be convinced we have learned something fundamental, if there is still no compelling theory?

  • Jack

    But if our results are consistent with w=-1, will we be convinced we have learned something fundamental, if there is still no compelling theory?

    Clearly the answer is “no”, which is one reason why I don’t believe that w is -1. The big problem with a true CC is that its energy density remains resolutely small no matter how far back in time we go. That would doom us to finding an infrared solution of the problem, and that’s just too hard. A value of w just a bit above -1 immediately means that the density blows up if you go back far enough, taking you back into a regime where you have some hope of bringing theory to bear. I know that Sean knows that there are problems with quintessence, but I still think the problem is too hard unless we can somehow get the dark energy density to be high early on. So I vote for w = – 0.95 [!] For the same reason I don’t believe in phantoms, though I know the SN data strongly point that way……..

  • Mark

    Hi Jack. I certainly echo your frustration if w=-1. I have different reasons though.

    The thing is, the CC really is small (possibly zero). Because of this we already have a fiendishly hard problem to deal with, even if we have no cosmic acceleration. Given how little we know about the CC, I don’t know if it is any harder ultimately to get a tiny nonzero one rather than one that is exactly zero. In this sense, if w is not -1, then you’ve always got the CC problem to solve plus the origin of cosmic acceleration.

    One other small thing. I wouldn’t say phantoms are strongly indicated by the supernovae data. There is plenty of room in the error contours for w=-1 or w>-1. The central value is ever so slightly less than -1, but in an entirely statistically insignificant way.

    What frustrates me about the possibility of the answer being a true CC is that it would, assuming GR is fine, be entirely nondynamical, and therefore we would have no hope of getting more information about it through either its time evolution or its spatial clustering.

  • Arun

    Testing the less than sign

  • Clifford

    I’m puzzled about the conclusion that w=-1 is not nice, or frustrating. I think it would be great if it were truly CC because it challenges theory so very much. From such challenges arise true revolution. I want it to be -1 so that we are forced to confront our poor understanding of spacetime and the quantum mechanics thereof.



  • Mark

    Hey cvj. It seems to me that the fact that the CC is already tiny (maybe zero) already challenges theory in deep ways. I tried to explain why, from an experimentally testable point of view, it might be frustrating.

  • Moshe Rozali

    My feeling is also that w=-1 is the most plausible option, purely as a theoretical prejudice: as far as I know, within the framework of EFT that we know and trust, any other option requires either more fine tuning than the just the CC (many times some functional fine tuning), or using the EFT where it is not clear it is valid (e.g adding all kinds of nonlocal effects). So the conservative instinct is to assume that nothing more crazy than necessary is going on. Of course conservative instincts are not the way to make progress (but I digress…).



  • Clifford

    Mark, I think that tiny is much harder to explain than exactly zero. So the challenge is magnified into a wonderful crisis. Crisis=opportunity. -cvj

  • subodh

    In response to Sean, concerning hep-th/0503158– this paper shows more than the alpha dependence of the Casimir force, it shows how it can be derived without references to zero point energies, rather, as a one loop process in QED (and hence sensitive to vacuum physics). The usual derivation is shown to be but a tidy mnemonic, and so, strictly speaking, the existence of the Casimir force cannot be taken as conclusive proof of the realness of zero point energies. Zero point energies are not the same thing as the fact that the vacuum can be polarized (giving running couplings, lamb shifts, anomolous magnetic moments etc.), though they are related.

    Anyways, theres a mountain of circumstantial evidence that suggests that zero point energies are real, and my favourite one is that we basically have no idea how to formulate QFT without them… but to get back to the point, you are absolutely right Sean that this is a digression… the real crux of the cosmological constant problem is the gravitational effect of these zero energies… so here goes:

    I’m curious about the following: we know that 70% of the universe is in the form of a non-clustering component with equation of state w, probably somewhere between -1.2 and -0.8. But we know that w = -1 matter does not redshift, wheras w

  • subodh

    to finish the last post… which somehow got chopped off…

    we know that w = -1 matter does not redshift, while w > -1 matter does redshift, and w -1 fluid. If the dark energy fluid is strictly non-clustering, then doesn’t it have to be a cosmological constant (w=1)?

  • Shantanu

    I have a different question. what do people think is the cold dark matter candidate?
    after evidence for dark energy people seem to have forgotten about
    the dark matter problem, even though it is very much there and as of
    now there is no laboratory evidence for ANY proposed cold dark matter
    candidate. also the no of speculated dark matter candidates is much more
    than no of proposed solutions to dark energy problem. so maybe
    we should take a different vote here : what do people think is the cold dark
    matter candidate from the options below?
    1)WIMP (SUSY neutralino)
    5)right-handed neutrino
    6) Branon
    7)MeV dark matter (proposed to explain the INTEGRAL results)
    8) mirror dark matter
    9) primordial black holes (my understanding is that they could be cold
    dark matter candidates, though am not 100 % sure)
    10) Q-balls
    14)dark matter from split susy
    15)kaluza-klein excitations
    16) sneutrino
    17) other possibilies

    Anyone here would like to make bets as to what which among the above
    is the cold dark matter candidate


  • Clifford

    I demand that there be chocolate truffles on the list. (see comment 22).

    My favourite is a supersymmetry partner. Number 1) on your list. -cvj

  • Mark

    Shantenu – a good and important question. People certainly haven’t forgotten about dark matter. There are many ongoing theoretical and experimental efforts to understand its nature.

    I tend not to participate in bets about science, since I tend to think that we just have to work hard and let nature guide us. There is an appealing broad theoretical argument that gives hope (but that’s all, mind you) that the dark matter might be the kind of WIMP that will be accessible to the next generation of colliders.

    The argument goes – the hierarchy problem of particle physics (why the scale of the weak interactions is so much lower than the scale of gravity) can be addressed by introducing new physics (particles and symmetries) at the TeV scale. An example of this (although the principle is much broader than this example) is supersymmetry. These new particles are related to the standard model particles through the symmetry. In order to satisfy precision tests of the electroweak theory, and other constraints, such as proton decay limits, one typically must introduce an extra symmetry that distinguishes all the new particles from the SM ones.

    This inevitably means that there is one of the new particles that is stable, because it is the lightest new particle and so can’t decay into other new particles (which are heavier) or SM particles (because of the new symmetry). Often this particle is neutral, making it a neutral, weakly-interacting particle with a TeV-scale mass (a good WIMP candidate).

    The point here is that there are good particle physics reasons to introduce some new particles and symmetries and that a natural outcome is a WIMP. It then becomes a detailed matter whether any given candidate is produced in the right amount to yield the observed dark matter abundance.

    I am fond of this general argument, but nature is in no way required to take that into account, and so I’m holding out for the data and working hard.

  • Peter Erwin

    Arun wrote (way up near the top):

    It seems almost anthropic that the 25% clumpy dark matter all lives in the galactic halo, and not in the galactic disk where we live.

    Actually, the dark matter is generally supposed to be distributed throught the halos of galaxies, including the part of the halo occupied by the disk. It’s apparently not as concentrated toward the centers as the baryonic matter (stars, gas, dust, planets, etc.) is, but there certainly should be dark matter in the disk. Searches for dark-matter candidate particles are based on that assumption (if there wasn’t dark matter in the disk of the Milky Way, you wouldn’t have a hope of finding it in your laboratory).

  • Sean

    I’ll agree with Mark’s argument, which is pretty much conventional wisdom. Supersymmetry (broken at the electroweak scale) is interesting for reasons having nothing to do with dark matter, and the imposition of a simple symmetry (R-parity) both helps get rid of some unwanted interactions, and makes the lightest supersymmetric particle stable. It then naturally has the right parameters to be the dark matter. So it’s certainly the leading candidate, but just as with dark energy, there’s every reason to keep an open mind and continue to consider alternatives.

  • Mark

    Other examples are extra dimensions (and the associated KK-parity) and the Little Higgs models (with T-parity)

  • Jack

    Mark said:

    One other small thing. I wouldn’t say phantoms are strongly indicated by the supernovae data.


    I think [correct me if I'm mistaken] that there is a consensus that the SN data *alone* do point to a phantom. It’s only when you combine the SN data with other things that Lambda moves back to center stage. But as I said I don’t believe in dark energy densities that get *more* negligible as you go back.

    Clifford said:

    I’m puzzled about the conclusion that w=-1 is not nice, or frustrating.

    Would you think it “not nice” if the LHC finds nothing but the standard model? That’s about as not nice as it gets! Observations showing w = -1 are not going to help theorists any…..

  • Mark

    I think you’re mistaken Jack. It is true that the SN data alone yield a central value that is certainly less than -1. However, since w=-1 and some values of w>-1 are easily within the 3-sigma error bars, we would not say that they point to a w

  • Risa

    I’m with my co-bloggers here: I’ll put my money on either a WIMP or chocolate truffles. But then again, I couldn’t tell a wimpzilla from a simpzilla if I met them on the street. BTW, I don’t think that primordial black holes can comprise most of the dark matter.

  • Clifford

    Risa, wouldn’t anything ending in “zilla” be smashing said streets and accompanying buildings? So I daresay you’d recognize them! -cvj

  • Mark

    Because it’s a WIMPzilla, its hands and claws pass right through the buildings.

  • Clifford

    Touche’! -cvj

  • Shantanu

    Thanks to Mark and other for the detailed replies. However an equally
    convincing particle physics argument can also be given for the axion.
    (and same for other candidates mentioned above). let me ask some more specific questions?
    1) is it possible for cold dark matter to consist of more than one component?
    2) is it possible from LSS+CMB+other astrophysical observations to put some constraints on mass and
    cross-section of CDM particles. or at least whether we can pin down
    whether CDM is a thermal or non-thermal relic. or is it that the formation of LSS
    is totally independant of the details of CDM. the only paper which I found
    some discussion about this is astro-ph/0309621 . but maybe people on this
    forum can clarify. after all the small scale hydrodynamic properties
    of different DM particles should be different.

  • Mark

    Shantenu, I would say that man of the examples on the list fall into the categrory I mentioned. Of the othere, I agree that there are probably as compelling arguments for the axion and for superWIMPs. I find the rest less compelling. However, as I hope I’ve made clear – nature is in no way required to follow what I, or anyone else, finds compelling, and so I think is is important to have people working out the details of all the ideas.

    As for your questions. The logical answer to the first is certainly yes. I think Joe Lykken was the person I once heard commenting that if we were made of dark matter, and knew that there was a portion of the energy budget of the universe that was baryonic, we’d be surprised to find how rich it was when we ultimately discovered the particle content of the standard model. Nevertheless, it is worth commenting that in beyond the standard model theories designed to address particle physics issues (e.g. SUSY, extra dimensions) one usually just gets a single thermal relic that is important.

    I have less to say about the second question. It might be that astrophysics on the scales necessary to make progress here will swamp any particle physics signal, or that making such detailed measurements is not feasible. I’m not expert on that, but hopefully one of our other commenters is.

    Risa? Simon DeDeo? Sean?

  • Simon DeDeo


    “One other small thing. I wouldn’t say phantoms are strongly indicated by the supernovae data. There is plenty of room in the error contours for w=-1 or w>-1. The central value is ever so slightly less than -1, but in an entirely statistically insignificant way.”

    One thing I heard recently (I haven’t had the chance to check it out myself) is that if you take all the data, and then take out the supernovae results, the errors actually get smaller. Something definitely odd is going on with the supernovae — or with everything else. It’s too bad that the original WMAP papers restricted w to be greater than -1 in their analysis.

    Doug Finkbeiner is our local DM annihiliation guru, and he suggests that a series of different results from different people (including his own dust map work) suggest something is going on in the TeV range or so. (The INTEGRAL results are something different entirely.)

    Re: learning about dark matter. There was a lot of fun when some folks (I think Steinhardt and Spergel were the first, but that may be my local bias!) starting talking about self-interacting DM as a way to explain the missing small scale power. As I understand, the more they looked at it, the more arbitrary some of the assumptions became. These days, the small scale power problem (I think) may or may not exist, depending on whether you are writing a paper about it or not.

    Various things (one being just simple homogenous cosmology — when do things decouple, etc.,etc., and another being the spectrum of the CMB — you can get energy injection from DM annihilation which can distort it) put constraints on the mass and cross-sections of DM particles (Padmanhaban and Finkbeiner’s recent paper talk about this a little.) I think I remember from a few years ago at a conference in Oxford that Joe Silk’s group — who were interepreting the INTEGRAL signal as MeV dark matter — had to play some games (not necessarily bad ones) with the energy dependence of the cross-section in order for things to work out properly.

    I haven’t thought about this carefully in a few years, however.

  • Gordon Chalmers

    Can someone describe why cold dark matter in the MeV range is ruled out? Are there references?

  • Simon DeDeo

    I think MeV CDM is still alive and well, if not perhaps on the lacrosse team like some of the cooler DM models that get all the attention.

  • Gordon Chalmers

    What about neutrons?

  • Mark

    Neutrons can’t be dark matter. The baryonic content of the universe is constrained by nucleosynthesis and the CMB.

  • Gordon Chalmers

    You are referring to the standard models of nucleosynthesis when you say that, I infer.

  • Mark

    As opposed to what Gordon? And what about the CMB?

  • Gordon Chalmers

    I dont know all the CMB data or the extensions of thenucleosynthesis theory so I cant say.

  • Jack

    Simon said:

    One thing I heard recently (I haven’t had the chance to check it out myself) is that if you take all the data, and then take out the supernovae results, the errors actually get smaller. Something definitely odd is going on with the supernovae — or with everything else.


  • Shantanu

    Thanks, Mark for the replies. Now let switch the topic back to the
    title of this thread and ask a question :-)

    In almost all papers which I read on estimating dark energy or constraints
    on dark energy(from present observations) how come very few of them refer to Daly’s work on estimating cosmological paramteres using double radio galxies. AFAIK , the first evidence for accelerating universe from double-radio galaxies (astro-ph/9803265) was around the same time as SN results.
    Sean or Mark , any comments? Is it because these systematics are not
    well understood?

  • Doug

    Jill wrote:

    To get back to Mark’s question—my wild guess is that we would get a better understanding of what w should be if we could work out what the hell is going on here:

    I say that because my guess is that to understand dark energy we will need a better understanding of the global structure of space time. You know, if the Universe has some weird shape [as in the recent Land/Magueijo stuff] that has got to tell us something big. OK, I’m just parroting what my boss said, but he sure made it sound convincing…

    Well, Mark’s question was how can we measure w, which, he reminded me, is not a theoretical question. However, Jill makes the same point I tried to make: the question assumes that DE is an inherent part of an otherwise consistent model of the cosmos. We just need to fit it into the model.

    Smolin argues that we need to get rid of background structure in our theories altogether, while Jill’s boss thinks that we need a better understanding of the background structure we’re using before we can understand dark energy. In the meantime, because we measure the geometry of the universe as flat, we estimate a value of DE based on this observation and an estimate of hypothesized dark matter.

    Now, Copi et al points out some disconcerting Gaussian and isotropic anomalies, while Richard Lieu has just published a paper in the “Astrophysical Journal,” showing that the CMB data contains no evidence of gravitational lensing. If the CMB radiation has come so far to inform us of the big bang, but yet did not encounter enough mass on the way here to lens it, we have another big problem in our modeling efforts. Lieu says, “There appear to be no lensing effects whatsoever.”

    So, are we going to adjust the Hubble constant, the estimated amount of the hypothetical dark matter, or some other parameter of the model to make things fit better? How would a change in the value of dark matter affect the value of w?

    Maybe, we need to start thinking that the CMB is not what we have supposed it is after all? Wow, now that is not likely to happen, is it? One thing for sure though, Jill is right on: “We would get a better understanding of what w should be if we could work out what the hell is going on here.”

  • Gordon Chalmers


    Here is another formula regarding the quark masses.

    to an approximate one percent:

    m_q = 10^{n-4} +/- 2^m 5^i 10^{-3} GeV


    10^{n-1} +/- 2^m 5^i MeV n=1,2,ldots 6

    5^{n-1} 2^{n-1} is the general form

    ~ n m i – +
    u 1 0 0 0 0 (with -)

    d 2 0 0 0 0

    c 4 2 3 1 5

    s 3 1 2 1 3

    t 6 2 7 5 9 (top) (with -)

    b 5 1 5 4 6

    (comment: 27 numbers out of 999 are 2^m 5^i)

    This formula works to one percent globally, and the +
    and – refer to m+i and m-i.

  • Gordon Chalmers

    Oops. The d and u has m=1.

    It seems to be quantization with two contributions, to a high accuracy.

  • David

    Can someone give an expert opinion on the paper by Cooperstock and Tieu,
    “General relativity resolves galactic rotation without exotic dark matter”,
    astro-ph/0507619 ?
    To a non-astro person like myself this seems a pretty big deal if it is correct…

  • Doug

    The paper is here:

    General relativity resolves galactic rotation without exotic dark matter

    I too am really anxious to hear from the experts on this. Can you imagine what eliminatiing dark matter from the picture will do? Dark energy now gets bumped up to about 97%, right? Sean, you’ll have to redo all those pie charts! LOL.

  • Arun

    Doug, I think a lot of astrophysicists will be kicking themselves if it turns out General Relativity is relevant in galactic dynamics. But it doesn’t seem intuitive either.

  • Sean

    Sorry, I meant to reply to this. I haven’t read the paper (astro-ph/0507619) in detail, but there are enough warning signs that I won’t bother. First, the Newtonian limit is extremely good for galaxies; corrections will be of order stellar velocities divided by the speed of light, which amount to 0.1% at best. And as gravity gets weaker, the corrections become less important — the opposite of what you would need to explain away dark matter. Second, there are mistakes that are easy to spot — e.g. you can’t choose the four-velocity to be given by eq. (2), since it wouldn’t be correctly normalized in the metric given by eq. (1). I don’t know where the important mistakes are, but they must be there.

  • Doug

    But Sean, what about his “gravitationally bound” argument for non-linearity, which he says “applies to the stationary (non-time dependent) case,” even when the field is weak and the motion non-relativistic?”

    Does the fact that the constituent stars of the galaxy are large rotating systems that contribute to the field, unlike the constituent planets of solar systems, play into the non-linearity of the field equation so significantly, as he claims?

    He writes:

    Since the field equation for rho is non-linear, the simpler way to proceed in galactic modeling is to first find the required generating potential phi and from this, derive an appropriate function N for the galaxy that is being analyzed. With N found, (12) yields the density distribution. If this is in accord with observations, the efficacy of the approach is established.

    Equation 12: (N2r+N2z)/r2 = (8piGrho)/c2

    If the non-linearity argument fails, then it doesn’t matter, but if it holds, then is this approach valid, as he claims?

  • Doug

    Hello? Sean, Mark? Is there anybody out there?

  • Arun

    The metric outside a compact body of mass M and angular momentum S is
    roughly, in spherical coordinates:

    ds^2 = (1- 2M/r) dt^2 – dr^2/(1- 2M/r) – r^2 ( dθ^2 + sinθ^2 dφ^2)
    + ( 4S sin&theta)/r^2 ( r sinθ dφ) dt

    The last term is non-Newtonian and resembles the term with the function N
    from the paper. A rough estimation of its value at the periphery of a
    galaxy shows it to be much smaller (by v/c, where v is an average stellar
    velocity and by geometric factors – most of the mass contributes very
    little to the angular momentum) than the Newtonian potential M/r.

    I translate the main claim of the paper to be that the periphery of the galaxy is higly non-Newtonian, and motion is dominated by the angular momentum term. The non-linearity claim I translate to the claim that the frame dragging term accumulates as one moves from the center of the galaxy to the periphery until it dominates the Newtonian potential. I do not know enough yet to be able to readily rule it out.

  • Sean

    The non-linearity argument fails. Again, you are in a regime where the deviations from flat space are extremely small, and linearization is perfectly okay. Corrections are of order the perturbation squared, which are incredibly tiny. If nonlinearities are ever important, they are important when gravity is strong, not when it is weak. Even in the presence of angular momentum, the weak-field GR equations are quite accurate; it’s a standard homework problem.

  • Arun

    Hehe, then obviously the exercise answer is not in any easy place for the authors of the cited paper to find.

    Anyway, I see that the paper has been submitted to the Astrophysics Journal. How do referees deal with such?

  • Doug

    I find it hard to believe that that Cooperstock and Tieu have made such an elementary error. I don’t think we are addressing the real issue here. As I read it, they are asserting that the non-linearity arises unexpectedly because, with the use of co-moving coordinates, w acts differently. In note 7, they write:

    7Normally, the fall-off of w with R = (r2 + z2)^-1/2 is used to derive the total mass of an isolated system. However, w is constant in this system of coordinates by (9) and we cannot do so here. The w constancy does not imply that that the mass is zero. In other (non-co-moving) coordinate systems, w would be seen to be variable. With the field being weak and the system being non-relativistic, the mass is well-approximated simply by the integral of p over coordinate volume.

    The constancy of w seems to be the key to their argument for non-linearity, so if non-linearity fails, as Sean asserts, is it because their argument for the constancy of w fails? They write:

    It is to be noted that it is the freely gravitating motion of the source material (the stars) in conjunction with the choice of co-moving coordinates (2) that leads to the constancy of w within the source. Had there been pressure, w would have been variable… the non-linearity of the galactic dynamical problem is manifest through the non-linear relation between the functions rho and N. Rotation under freely gravitating motion is the key here. By contrast, for time-independence in the non-rotating problem, there must be pressure present to maintain a static configuration, N vanishes for vanishing w and del^2w is non-zero yielding the familiar Poisson equation of Newtonian gravity.

    Is this a valid argument or not? If not, why not? It seems to me that we are trying to dismiss their argument rather than trying to answer it.

  • Arun


    What is the physics (as opposed to what is the math) of what the authors are arguing? It is that the rotation of the galaxy provides a contribution to the metric that is much stronger than the Newtonian contribution. Based on what we know about gravity and various weak field expansions that exist for GR, this is implausible. How do effects that die off at (1/r)^2, and or faster sum up to exceed the (1/r) contribution? Moreover the source of the (1/r)^2 effects is v/c smaller than the source of the (1/r) contribution.

    Absolute certitude requires redoing the calculation independently. For something very implausible, it is not worth the effort, at least, for someone like Sean. However, it may be a good exercise to give students.


  • Doug


    I think that they are arguing that what you are asserting is true in the usual analysis, but when the co-moving coordinates are used in the analysis this causes w to remain constant at 0 and consequently the field equation becomes non-linear. The justification of this approach comes from the notion of a “gravitational-bound” system, whatever that means. The upshot is that, not withstanding the weak galactic field, the galactic dynamics are non-linear:

    …insufficient attention has been paid to the fact that the stars that compose the galaxies are essentially in motion under gravity alone (“gravitationally bound”). It has been known since the time of Eddington that the gravitationally bound problem in general relativity is an intrinsically non-linear problem even when the conditions are such that the field is weak and the motions are non-relativistic, at least in the time-dependent case. Most significantly, we have found that under these conditions, the general relativistic analysis of the problem is also non-linear for the stationary (non-time-dependent) case at hand.

    I can’t argue the merits of this assertion. All that I can do is ask that someone who can do so. So far, I don’t think anyone has, have they?

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  • Arun

    Authors: Mikolaj Korzynski


    Recently a new model of galactic gravitational field, based on ordinary General Relativity, has been proposed by Cooperstock and Tieu in which no exotic dark matter is needed to fit the observed rotation curve to a reasonable ordinary matter distribution. We argue that in this model the gravitational field is generated not only by the galaxy matter, but by a thin, singular disk as well. The model should therefore be considered unphysical.

  • Gordon Chalmers

    Recall the mass formula 10^i GeV + 2^j 5^k MeV, with almost exactly 5% of the contribution to the fermions coming from the latter. 20/21 is 95.2% and this ‘number’ fits almost exactly the dark matter proportions. Couldnt there be a bright explanation of this in the ‘dark matter’ context? The blog as a research tool; it seems reasonable with two Higgs or instantons.

  • Gordon Chalmers

    Perhaps the ‘experts’ will offer an opinion on these seeming fortuitous numbers?

  • Shantanu

    Sean and/or Mark and others, how about to my question about using
    radio galaxies to measure dark energy?

  • Sean

    Shantanu, it’s just that the error bars were very big on that measurement. It wasn’t enough to say that the universe was accelerating, only that there wasn’t enough matter to provide the critical density. And there were a lot of such measurements, albeit also with substantial error bars. It was one piece of the puzzle. Nowadays, we think that supernovae or other methods are more precise.

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Cosmic Variance

Random samplings from a universe of ideas.

About Mark Trodden

Mark Trodden holds the Fay R. and Eugene L. Langberg Endowed Chair in Physics and is co-director of the Center for Particle Cosmology at the University of Pennsylvania. He is a theoretical physicist working on particle physics and gravity— in particular on the roles they play in the evolution and structure of the universe. When asked for a short phrase to describe his research area, he says he is a particle cosmologist.


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