Of Particular Significance

Dark Matter Debates

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 05/27/2014

Last week I attended the Eighth Harvard-Smithsonian Conference on Theoretical Astrophysics, entitled “Debates on the Nature of Dark Matter”, which brought together leading figures in astronomy, astrophysics, cosmology and particle physics. Although there wasn’t much that was particularly new, it was a very useful conference for taking stock of where we are. I thought I’d bring you a few selected highlights that particularly caught my eye.

Does Dark Matter Exist, and In What Form?

First, the question of whether dark matter even exists was nicely explored by Stacy McGaugh, from the University of Maryland, who gave a talk on the possibility that the laws of gravitation and/or motion are altered, along the lines suggested by Mordechai Milgrom. The theoretical approach of Milgrom is usually called “MOND”: MOdified Newtonian Dynamics; it involves an ad hoc change in the laws of motion when objects exceed a certain rate of acceleration. McGaugh, who is an astronomer, gave a careful illustration of how MOND à la Milgrom explains some odd features of galaxies. This involves careful examination of how stars rotate around the centers of galaxies of all sizes, from the very large to the very small. He emphasized that the hypothesis that galaxies are made mostly of dark matter, and embedded within a large clump of the stuff, does not easily explain these features (though interestingly professor Alyson Brooks of Rutgers University mentioned that her simulations of galaxy formation, which assume the presence of dark matter, do actually reproduce one of these features.) He also showed that, by contrast, MOND doesn’t do well at all with certain cosmological data, especially in properties of the cosmic microwave background. It was nice to see the evidence for and against MOND laid out in a single, well-delivered talk; it’s important to look at this question in an even-handed way, so that both the weaknesses and strengths of the dark matter hypothesis are clear.

But in his Wednesday evening talk, the famous astrophysicist and cosmologist Jim Peebles pointed out just how broad is the cosmological evidence for dark matter, from a wide variety of independent sources. He views the basic notion of dark matter as an idea that is not just widely accepted, but has been established by data. But he also suggested, alluding to the many puzzles about galaxies (some of which were mentioned in McGaugh’s talk) that we should view our understanding of galaxies and how they form and evolve as still quite poor, with room for significant surprises.

Unfortunately, not that much time was spent during the conference on the possibility that dark matter is in the form of waves in a type of field called an axion. And almost nothing was said about the possibility that dark matter is made from other types of objects, such as primordial black holes.  But I guess one can’t cover everything in a 3½ day conference…

So Many Hints, So Little Time

A lot of the presentations, discussion and debate concerned the hints of dark matter that have been coming and going like clouds on a windy day.

Anyone who still believes, after the limits from XENON100 and the devastating blow from LUX, that the hints of dark matter seen by DAMA/LIBRA, COGENT, CDMS, CRESST, etc. might be due to something real now also has to confront the non-observation of any such hint by Super-CDMS — an upgrade of the CDMS detector.  While not as powerful as LUX for large-mass particles, Super-CDMS is both more powerful and more robust for detecting dark-matter particles with masses in the 2 – 10 GeV range.  LUX and XENON100, which use liquid xenon as a target, are very different in their technology from the experiments that see hints.  These all use solid targets made mostly from smaller atomic nuclei than xenon, and this could allow one to dream that dark matter is of a sort that would show up in experiments such as DAMA more easily than in xenon-based experiments. But Super-CDMS uses a germanium target, and germanium nuclei are quite a bit lighter than xenon nuclei; so this argument is no longer so persuasive.  Yes, it is still perhaps possible to imagine dark matter that would give hints at DAMA/LIBRA or COGENT and escape both the xenon experiments and Super-CDMS; but it is looking increasingly contrived.

Result from super-CDMS from late February, shown at Dark Matter 2014. Plot shows dark matter scattering rate versus the dark matter particle’s mass; all regions above the solid and dashed lines are ruled out, according to the experiment labeling the line. Hints of dark matter are shown in the orange, blue, pink and yellow regions. (The green regions can be ignored by non-experts.)  All of the hints are ruled out by both LUX and Super-CDMS (marked “This result”). Explanations for the hints that evade both LUX and Super-CDMS are not easy to come by.

Meanwhile, the possibility of dark matter annihilating in the center of the galaxy and resulting in unexpected numbers of positrons is suggested by an unexpected number of positrons, relative to electrons, at energies of 10 – 300 GeV. This effect was first noticed by the PAMELA experiment, and then confirmed by FERMI, after which it was carefully measured by AMS. But is this effect from dark matter, from pulsars [for a definition, see below], from supernova remnants, or just simply from cosmic rays? There were three very different talks on this question, with very different viewpoints.  Personally, I wouldn’t bet on dark matter here…

Yet another hint of dark matter — an excess of photons of energy of about 130 GeV or so from the center of the galaxy, seen in the data from the Fermi satellite — appears to be going away, despite having reached 5 standard deviations of significance by someone’s measure. Among those saying so is Christoph Weniger, the researcher who first identified this excess a couple of years ago. It isn’t clear yet whether the excess was a statistical fluke or a detector problem — the significance of the signal has gone down both because of a reanalysis by Fermi of their data and because there have been no events at 130 GeV for many months. Either way, it seems to be gradually disappearing as more data is collected, and while its cause may become clear in a few years, all we can say for now is “R.I.P”.

Hint Du Jour Number 1

But two other hints of dark matter are alive and … well, not dead yet. The first involves an excess of photons (i.e., more photons are observed than expected) in the 1 – 10 GeV range, originating from a region of the galaxy that extends outward a very substantial distance from the center of the galaxy. These photons, first identified by Goodenough and Hooper here, and most recently explored here, may be a signal of dark matter particles annihilating. (Specifically, when they annihilate they may produce a quark and an antiquark, which in the end produce multiple hadrons, some of which can decay to photons.)

However, these photons might also be due to something astrophysical. So far, the only known astrophysical candidate is a horde of millisecond pulsars. What are those? A neutron star is a giant balls of neutrons, about 20 kilometers across, that is a remnant from a Type II supernova explosion.  A pulsar is a neutron star that has a strong magnetic field and sends beams of electromagnetic radiation into space as it spins; since these beams are only detectable to us when they point in our direction, we see them as pulsing, hence the name “pulsar”.  A millisecond pulsar spins 1000 times a second or so (wow!).  These objects can emit very-high-energy photons, as energetic as a few GeV, out into space.

The excess of photons have an energy dependence that looks a bit different from pulsars, but the peak of the distribution occurs at about 2 GeV and drops off around 10 GeV, which is just what pulsar photons would be expected to do.  That makes one immediately suspicious that pulsars are responsible.  That said, the wide distribution in space of these unseen pulsars, and the number of pulsars required, are perhaps surprising.  But pulsar experts tell me that so little is known about pulsars in that region that it would be hard to argue strongly against that possibility.

How can the two possibilities (pulsars vs. dark matter) be distinguished? If this same signal is seen in the dwarf galaxies that surround our galaxy, which should have very few stars but lots of dark matter, it might convince us that the signal is from dark matter and not from pulsars. Conversely, if it isn’t seen, it is more likely from pulsars.  Maybe.  Well, this hint isn’t likely to go away soon, nor is it likely to be diagnosed convincingly anytime soon, so we’ll hear more about it in future.

The Hint Du Jour Number 2

The second hint is from an excess of X-rays with an energy of just about 3500 eV; these have been identified in various galaxies and clusters of galaxies. (I wrote an incomplete article about it here; I still owe you a better one.) These X-rays are most popularly suggested to be from dark matter in the form of decaying sterile neutrinos (i.e. neutrino-like particles that are affected by none of the known non-gravitational forces, unlike ordinary neutrinos which are affected by the weak nuclear force.) However, as I emphasized to you from the beginning, the same signal could also arise from other types of dark matter. For example, if dark matter particles are, like atoms, able to be “excited” (i.e. able to absorb energy and become slightly heavier but unstable versions of themselves), then when two dark matter particles bump into one another, one might become excited, and later decay back to its original state while emitting an X-ray photon.

Alternatively, perhaps this excess is due to an unknown atomic effect, and has nothing to do with dark matter at all.  Again, seeing this excess in dwarf galaxies would be potentially crucial in deciding the issue.   Compared to galaxies the size of the Milky Way, dwarf galaxies have much more dark matter than hot gas, so these X-rays would be seen there only if they are due to dark matter, and not due to atomic physics.

Since either or both of these hints du jour might have to do with astrophysics, not dark matter, we are, yet again, in a waiting game — waiting for more data, and more convincing data, that might allow one or both of these sources of photons to be fully explained.

Looking for Dark Matter In New Ways

Finally, one of the most interesting things I learned at the conference was explained by professor Rouven Essig of Stony Brook University. He and his team has been working on the problem of detecting dark matter particles much lighter than those that XENON and LUX and Super-CDMS are designed to detect — as much as 100 to 1000 times lighter. XENON-, LUX-, COGENT- and CMDS-type experiments are best at detecting particles with mass of 5 – 1000 GeV/c², by picking up signals from the scattering of a dark matter particle off an atomic nucleus. But there’s a workable strategy, Essig argued, for picking up the scattering of a dark matter particle off an electron in an atom. Detecting dark matter particles with masses down to 10 MeV/c² could soon be possible in XENON/LUX-type detectors, and sensitivity to 1 MeV/c² might someday be possible in CDMS-type (i.e. solid-state) detectors.  This opens a new opportunity to look for dark matter in a form that previously would have slipped through our nets.

The Debates Will Continues

Though dark matter continues to elude our attempts to identify it, many experiments are continuing to seek this mysterious stuff, using a wide variety of methods. We can expect more hints of progress (most of them false alarms) over the coming decade. But can we expect an actual discovery? Only the heavens know.

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131 Responses

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  2. Phil, there are currently three active surveys searching for intermediate mass black hole dark matter, all of which started in the past couple years.

    There is only one paper which excludes IMBH dark matter (for the reasons you state, and not gravitational lensing which thus far has only ruled out MACHOs below 15 solar masses) and it was published in 2008.

  3. To study further, I have joined in the Tokyo University Course of the From ” the Big Bang to Dark Energy” which will cover various topics on the discoveries about how the Universe evolved in 13.7 billion years since the Big Bang.

  4. Neighbouring Dwarf Galaxies Refuse To Fit The Standard Model Of The Universe. by Forbes 6/12/2014
    The latest challenge comes from astrophysicist David Merritt of the Rochester Institute of Technology and his colleagues, who say that recent attempts to force dwarf galaxies to fit the standard theory are flawed.
    “The model predicts that dwarf galaxies should form inside of small clumps of dark matter and that these clumps should be distributed randomly about their parent galaxy,” Merritt said.

    Is it a new dark matter debate?

  5. What do you think about LSPs (Lightest SUSY Partners)? I have a friend who has completely dropped interest in SUSY, and thus the LSP solution, since the LHC saw no evidence of SUSY by the end of its last run.

  6. You, Dr. Matt Strassler, wrote on June 20, 2012 “Extra Dimensions & Newton’s Gravity”.
    You were talking about 5 or more dimension space. But in case 2+1 (or 3) dimensional space there is not “Inverse Square Law” but “Inverse Law” .
    It is interesting. You described 2 dimensional space with depth W which is like a slab.
    In galaxies stars are rotating by “Inverse Law”. Then we should have thought that your “slab” idea is valid.


  7. So, I believe the first evidence for “dark matter” was the observation that stars on the fringes of the galactic disks were orbiting the galactic nucleus much faster than expected. This expected value was determined by considering only the gravitational potential energy created by the luminous mass in the galaxy…

    This leads me to a question:
    In GR, if gravitational attraction can be caused by energy density in ANY form, is it possible that taking into account the rotational kinetic energy of the galaxy would help patch up any of this discrepancy? Or, vacuum energy density of any as-of-yet unknown fields? The Higgs field?

    1. But, I’m guessing that the problem now goes further than just this galactic orbital speed problem…
      I mean, what is the main motivation for belief of dark matter now?

      1. First observation of Dark matter was by Fritz Zwicky(1933) in the Coma Galaxy Cluster. Galaxy Clusters represent the bulk of mass-energy in the universe. But why does it have to be rest-mass? Neutrinos can take on huge kinetic energy. (Ice Cube’s three biggest hits.) Think of this as momentum, energy, or mass, it’s all equivalent.

        1. “But why does it have to be rest-mass? ”
          Because dark matter must be gravitationally binding – at least to the small scales of dwarf galaxies – to produce the effects attributed to it. As I understand, the kinetic energy of low mass particles is principally a product of velocities that can easily exceed the escape velocity of large scale structures such as galaxy clusters.

          1. Dwarf Galaxy (Segue1) dark matter is machos, brown to black dwarfs. The matter is cold and dark, but not utterly black.
            Galaxy Cluster is a gigantic ball of X-ray emitting matter (see Chandra website). They are megaparsec scale structures radiating at 100 million Kelvin and warping spacetime into gravitational lenses. They have a degenerate core. (arXiv:13076788v1) (Nieuwenhuizen/ Morandi 2013.) The core could be neutrinos. Or anything you like.
            JT you are absolutely right that Spiral Galaxy dark matter is nothing at all, except a misapplication of Keplerian orbits to describe a non-Keplerian system.

          2. This makes some sense… that the neutrinos are indeed not gravitationally bound themselves. However, I would imagine that the tremendous energy throughout the universe due solely to high-energy neutrinos can cause all OTHER matter to be bound much more strongly than expected.

            Sure, they’re not necessarily “dark” (ie. we detect them regularly), but interaction is so rare and (as lavaroy mentioned) they can take on PeV energy (and beyond), that I imagine neutrinos would satisfy the requirements of “dark matter”…

              1. LCDM is part of Big Bang Cosmology. Neutrino DM is the antithesis. It forces a rejection of the Big Bang. Degenerate neutrinos prevent a singularity.
                “The Pauli principle is not due to a force, but rather a consequence of the nature of the things themselves. If you try to make a state with two electrons doing the same thing, you will find that state equals zero; it’s not a state at all. So no physical phenomenon can violate the Pauli principle; NO AMOUNT OF PRESSURE AND GRAVITY can change it.”-Strassler
                “In a world with three or more space dimensions, there are two types of fields; ripples in boson fields (like photons) must be symmetrically related, whereas ripples in fermion fields must be antisymmetrically related. No force is required to make this so; it is in the nature of the ripples. Since antisymmetrically related objects cannot be in the same place doing the same thing, the Pauli exclusion principle applies to them.”-Strassler.
                (But, Strassler favors a field of the third type, for spacetime, called a relativistic field, a field with no medium, only metrics.)
                I say spacetime is a fermion field, and can not be subdivided infinitely (Planck) or crushed infinitely (Pauli).
                It does require neutrinos to be massless and flavorless and not Majorana.
                Give me a neutrino rest-mass, give me conserved lepton flavor, give me neutrinoless double beta decay, give me just one wimp, and I’ll give you LCDM.

      2. I meant frequency-energy E=hf. Neutrinos “store” energy as frequency, like photons. They transfer momentum-energy to nucleons when they score a direct hit, which is rare, but given enough time and neutrinos, you get hits.

          1. … I think they typically have energies to high to be considered “bound”. Am I wrong here?

    2. Yes, exactly. Rotational kinetic energy of spiral galaxy, swept under the rug, is the discrepancy. Assuming a spiral galaxy will have Keplerian orbits is assuming it formed from a static, collapsing gas cloud. Instead, let’s assume spiral galaxies form by a pair of dwarf ellipticals falling into each other. What do you get? Outer stars with correct speeds. And a nice trail of bright blue young stars in the wake as the halos compress each other.

      1. Lavaroy –

        What do you mean by “correct speeds”?

        Correct, as would be expected from just the fermionic galactic matter (which DOES NOT agree with observation, from what I understand)? Or, correct, as agrees with the observation that the bodies on the fringe of the galaxies orbit much faster than expected?

          1. Really? This alone solves that problem? How can they have these speeds while still being gravitationally bound?

            Sooooo, I’m guessing the real debate goes much further than this now, if this is the case.

    3. “stars on the fringes of the galactic disks were orbiting the galactic nucleus much faster than expected. ”
      But moreover!
      The flat rotation curve of spiral galaxies is the observation fact. Then dark matter is assumed to exist. But why flat? Dark matter should distribute in a certain form in order to make the rotation curve flat? I think “flat” is a very peculiar requirement. It can be ascending or descending depending the dark mater distribution. So again, why should dark matter have a virtual characteristic of distribution which makes the rotation curve flat?

      1. Excellent comments! Dark Matter is nothing but a blind spot (in this case). Spiral Galaxy rotation is simply conserved angular momentum from a 2D or “slab” process.
        Dwarf Galaxy DM will turn out to be cold baryonic matter (machos).
        Galaxy Cluster DM will turn out to be degenerate fermions.

      2. I don’t think a “flat” rotation curve is mandatory…
        only that the curve does NOT fall off as expected from solely the visible matter.

          1. Dear Iori, the Dark Matter problem is linked to the Star Formation problem. Spiral Arm stars do not form by molecular clouds slowly contracting. In fact, no stars form that way. Clustered stars form when dust clouds get rammed by UV radiation, as observed in Eagle Nebula. Spiral Arm stars form when infalling dwarf galaxies impact each other’s dusty halo and create turbulence. Stars form in the vortices. Astrophysics does not acknowledge this because there is no mathematical equation for turbulence.

  8. Matt: do you know if videos of talks are going to be online?
    The last Sackler conference on tests of GR was.

    1. Everything was video recorded and I was told that these would be made available in due course.

  9. Quite a puzzle this dark matter. Don’t really buy into anti-quark nuggets, but do admire the attempt to respect the Law of Conservation of Baryon Number which many physicists have thrown under the bus. (Yea, they love symmetry; just as a man tells his wife he loves her from his mistresses’ house). I suggest that (1) we do experiments to directly determine neutrino mass. Do we “really” know that the sum of the 3 neutrino rest energies < .3eV? We sure act like we know, yet the KATRIN experiment (2015) plans to determine the rest energy of the electron-neutrino from the CURRENT 2.3 eV down to ~.02 eV. So apparently not everyone is so cock sure; maybe neutrinos do have enough mass to be the dark matter.

    Then there is the notion of mass itself. I suggest that (2) we do experiments to make sure that there really is just one type of mass; that the ratio of inertial to gravitational mass is indeed = +1 for many more particles than we have thus far tested. Do we “really” know that the ratio of inertial to gravitational mass is indeed = +1 for everything? We sure act like we know, yet the AEgIS experiment (2015) plans to determine the gravitational acceleration of anti-hydrogen. So apparently not everyone is so cock sure; maybe antihydrogen falls up(!), and IF (a very big IF) so then maybe other particles, like neutrinos have (even wilder) a ratio of inertial to gravitational mass that is neither +1 or -1 ,but 1.0×10^-6! (Yes, that would mean it might be possible to generate large gravitational, and antigravitational fields using very little inertial mass – something we NOW consider impossible).

    1. S. Dino: Neutrinos are probably the bulk of dark matter. They have two things going for them: They are matter, and they are dark! They may have vanishingly small rest-energy, but they can take on monstrous kinetic energy. Galaxy clusters, systems of colliding galaxies, are probably the accelerators. And that’s where Zwicky “saw” the dark matter. Forget wimps. Ice Cube has already detected dark matter in the form of three PeV neutrinos.

      1. Neutrinos are a bad match for every astronomical observation that suggests DM. Hot Dark Matter does not successfully reproduce the observed structure — it’s moving too fast, well beyond escape velocity for any concentration of mass this side of an event horizon. So Dark Matter clouds would not remain clouds and seed the formation of regular-matter structure, they would disperse. The higher energy the neutrinos, the more true this is.

        There are also strong arguments that there cannot be nearly enough total energy in neutrinos to account for DM observations.

        Neutrinos are undoubtedly a *kind* of Dark Matter, but they are probably not the Dark Matter we are looking for.

        1. It was recently explained that, like CMB photons, primordial neutrinos would lose tremendous energy. Unlike zero rest mass CMB photons, primordial neutrinos would also lose velocity – now travelling at speeds much lower than c. I don’t have the references cited to me handy, but a quick search reveals http://arxiv.org/abs/0712.1210.

        2. In my preceding innocuous comment – which has since June 9 been “awaiting moderation” for some reason and therefore may not be visible to others – I agreed with your issues regarding neutrinos as dark matter. However…

        3. Dear Anon, I agree neutrinos don’t work, if they are considered to be hot particles flying around. As you say, they must be confined behind an event horizon. That is what I mean by Zwicky Dark Matter. Neutrinos are the mass in supermassive black holes and galaxy clusters. arXiv1307.6788v1
          (I agree neutrinos are not the dark matter in dwarf galaxies or spiral galaxies.)

  10. Is there information available which describes how different stellar rotation period stars are distributed around Milky Way? Do stars rotate faster (in general) if they are closer to the galaxy edges?

  11. The LUX experiment, which has found zilch in the way of Dark Matter, is a liquid based experiment,

    The DAMA, Cogent, et al, experiments which involve cryogenically frozen crystals with the constituent atoms (and nucleons) in the lowest energy state, and almost absolutely motionless, always find evidence of Dark Matter.

    The Xenon based experiments, which involve Xenon in a liquid state, that is, with Xenon atoms (and associated nucleons) possessing three degrees of freedom, never, ever find a trace of Dark Matter.

    It is time to stop debating this at the level of the clever people who attend seminars such as the Harvard-Smithsonian conference. The physicists who attend such conferences can only reason within the framework of the physics paradigm firmly entrenched and nurtured within the confines of their skulls.

    I suggest, instead, that we should ask a selection of 12 year old students, just starting out on their first physics and math courses, to suggest a possible solution to this conundrum.

    I’d put my money on the 12 YOs.

    1. Your statement isn’t really correct. The experiments in question find *hints* of dark matter; none of them show strong evidence except DAMA/LIBRA, and they find it in a specific way that’s unique to them. And physicists understand perfectly well how this can happen: it’s called “not yet understood backgrounds to the measurement.” We see it all the time, in every field of study.

      You can put your money on the 12 year olds. I’d be happy to bet you my entire year’s salary. Contact me if you want to set this experiment up.

      1. When the 12 year olds get to be 16-20 years old the probabilities might change significantly.

  12. the blog system cut out some lines – the end of the next to last paragraph should read

    (the) seismological data they had available set weaker limits for masses for masses less than 10^5 kg. The ultimate limit of this technique set by the flux, which declines with increasing mass, and so even decades of good seismology would be limited to masses less than 10^8 kg.

      1. Dear Philippe;

        Thanks very much for alerting me to this. (The basic idea here is that relatively small pieces of mica can be excellent detectors if they are exposed for half a billion years or more, as some are.) I had read some of Price’s papers and knew that Mica set the limit for very small masses, but somehow had never registered just how high in mass the limit extended. I recalculated the DM limit based on the data in http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1985ICRC….8..242P&defaultprint=YES&filetype=.pdf with the Planck 2013 cosmological parameters and an up to date Halo model and get a limit of 140 gm, very close to the older 160 gm limit.

  13. @Matt – Sure. A “quark nugget” (a dense ball of matter with a density of order 10^18 kg/m^3) would have a very high mass to area ratio, and thus would tend to pass through ordinary matter, especially if it is supersonic to begin with (as a halo DM particle surely would be), In passing through (say) the Earth, a supersonic nugget would move matter out of its way, setting up a shock wave in the material, which, at a distance, would appear as seismic waves. Unlike a meteor impact or an Earthquake (or a nuclear explosion), all of which are more or less point sources of seismic energy, a quark nugget would cause a “linear earthquake” along the nugget’s path, which would be very distinguishable from a point source. The Apollo ALSEP lunar seismological array was state-of-the-art for its time, and Herrin et al used the ALSEP data to set stringent constraints on such nuggets, ruling them out as making up the dark matter for masses between ~ 10 and ~ 10^3 kg. They used the same technique for the Earth; the seismological data they had available set weaker limits for masses 10^8 kg.

    The limit for lower nugget masses is right now set by the MACRO neutrino experiment in Gran Sasso (which shows that masses < 10 milligrams cannot be the sole source of DM). Better limits could clearly be set by IceCube, as its volume is much larger, As it happens, the relevant data are being recorded, but there are (as yet) no firm plans to publish it (for this use). I have been talking to the people at the IceCube HQ at U Wisconsin about this, and hope to make it happen; we shall see. The IceCube data should be able to increase the lower mass limit on DM nuggets by at least 2 orders of magnitude, to about 1 gm, so it would be worth publishing (IMO).

  14. @Philippe – You can use an entire planet (such as the Earth or the Moon) to constrain condensed dark matter in part of that range (Macroscopic condensed matter particles larger than a milligram or so would easily pass through a terrestrial planet). The Moon is particularly seismologically quiet, which is useful for such studies; Herrin ( http://arxiv.org/abs/astro-ph/0505584 ) showed that the lunar ALSEP data could rule out condensed objects as the sole source of dark matter in the range 10 kg – 1 ton (10^4 – 10^6 gm), and that terrestrial seismology places a weaker constraint up to ~ 10^5 kg. The smaller masses that Ariel Zhitnitsky favors I actually think are at risk from being excluded by a combination of IceCube and other terrestrial data (but these have not been published yet); the larger (order 10^10 kg) masses that I happen to favor do not appear to be ruled out by any published data set.

      1. I guess the next question is “who ordered a quark nugget?”The growing list of fantasy DM particles boggles the mind!

        1. It’s not a new particle. Zhitnitsky makes the argument that maybe these chunks of unusual matter form from the particles we already know. It’s a long-shot argument; most people don’t believe that this happens. But there’s no harm in checking.

    1. Thanks Marshall for the precision. Actually I was aware of the limits inferred from seismic signals (total seismic energy in case of the Moon and search for epilinear seismic track for the Earth) but ignored them to keep things simple — since these limits are pretty weak, especially when considering that we could have a mix of many different quark nugget masses for composing dark matter. I am not aware of any IceCube constraint on this, though (would be interested to get more presisions on that). In the range 10⁻¹⁰ – 100 grams, the best constraints come from searches for tracks in ancient mica, and I doubt IceCube would be able to beat them. For masses > 10¹⁷ grams, there are constraints from gravitational lensing. But in between, it’s pretty much unconstained apart from the seismic results you mentioned. I saw your paper mentioning fast-rotating asteroids possibly containing a core of quark matter — very interesting.

      But my initial question was more directed towards theorists about the Zhitnitsky model of anti-quark matter…

  15. I am intruigued by a claim that a model of anti-quark nuggets (stable aggregates of anti-up, anti-down and anti-strange quarks) could at once explain dark matter and matter-antimatter asymmetry, as well as some of the X-ray and gamma excesses (see http://arxiv.org/abs/astro-ph/0611506 and references therein). It also appears that such objects are unconstrained by direct detection experiments in the range 100-10¹⁷ g. I would be interested to hear some informed opinion about that idea.

  16. If you run the clock back, I wonder how small the universe would have to be in order to have “wall to wall” dark matter.

    1. That probably never happened, actually. The dark matter was probably created in the decays or collisions of other, heavier particles that were present at even earlier times and were never wall-to-wall.

  17. Thanks again for extremely informative insights. I should be most grateful for your comments at greater length on sterile neutrinos and the neutrino minimal standard model, eg http://arxiv.org/pdf/0901.0011 and related papers. Is this all just too contrived to be a realistic candidate theory?

    1. It’s not too contrived; but I tend not to write about speculative ideas unless they’re really of huge conceptual importance, which, in my view, this one is not. Sterile neutrinos are nothing more than particles that (a) are fermions, (b) are unaffected by electromagnetic, weak nuclear and strong nuclear forces, and (c) combine with neutrinos to give the latter a mass. That’s all there is to them.

      1. Folks a plausible and self consistent explanation of Dark Matter and Dark Energy can be found in this paper http://www.worldscientific.com/doi/abs/10.1142/S0219887814500595
        MONDian behaviour in galaxies begins when the baryonic energy density at galactic edges is equal to the Dark Energy density.This equates to imply that the centripetal acceleration at the edges of galaxies is equal to the cosmic (Hc)acceleration (approximately =milgrom’s ac eleration constant).Unfortunately the paper is behind a paywall.

  18. Is there any up to date graph that would include allowed / expected cross sections and mass for SUSY wimps post-Higgs discovery?

    1. I don’t have one handy; certainly there are lots of papers on such things. Try looking at recent review talks on WIMP dark matter given within the last year.

  19. Dark matter is obviously primordial axion holes that alter gravity. Physicists, work out the details, I’m too busy channeling his new insight into healing crystals.

  20. Fermi above 130 GeV signal gone,
    This “signal” was very strange and for me it was clear that it was a detector or analysis bug. I guess I wrote it here or at Phils site and got some really strange answer ignoring my arguments. For example in the data with less counts at higher energy the failure was relative (not only absolutely) smaller? Just by the simplest experimental statistics it is clear that this is not possible. Strange that no one tested the data on this absolutely basic consistency before. I call the data BS, nice too see that I was right!

  21. Got to try one more which probably will be ignored, but here goes (and sorry for being off topic but I don’t know which article to ask it in);

    If intelligence can formulate the physics to understand nature (universe) then can physics explain intelligence?

    Are experiments and observations real?

    1. Experiments and observations must be real in that they are as real as our lives are, for that is what they are based upon. If we ask ‘is reality “real”‘ then we leave the realm of science. (It is possible we are all brains in a jar or only I exist But unless there is any way to tell then the propositions are unscientific.)

      Your first question is more interesting. In essence it is ‘Can something be smart enough to really understand itself?’ And currently, we just don’t know. We may never know.

      We can, in theory, at least if given the processing power and time, take our current physical models and reproduce nearly everything we see in everyday life, cars, the behavior of water drops intelligence… but there are many things we don’t know. Emergent properties make systems much more than the sum of their parts, subtle effects we don’t know about yet may complicate things. (What if intelligence is due to quantum tunneling? Or requires neutrinos?) These obstacles can in theory be overcome.

      Harder is whether we will ever be able to comprehend the ‘theory of intelligence’; already many things we could in theory understand are too complex for the brain itself to contain. (Try working out large prime numbers, computers can but your lifetime processing capacity is quickly exceeded.) Maybe the true nature of the universe requires a type of thinking which we simply cannot do or is too complex for us ever to discover.

      And finally of course you have supernatural explanations, I think most of them rule out understanding ‘the soul’ from square one.

      All we can do is try, and maybe we’ll succeed.

  22. Could this analogy be accurate?

    ocean ~ universe (all energies, including dark energy),
    waves ~ dark matter,
    whitecaps ~ visible matter

    Which leads me into a more broader question, is the universe really expanding or is space oscillating like a elastic liquid filled balloon?

    1. The analogy is interesting; ocean foam interacts but weakly with waves and there is some relation between them.

      However, how exactly would space be osculating ‘like a liquid filled balloon’? We are quite sure that at large scales the space between objects is expanding and has been since the year dot. If you are saying this expansion is akin to the rarification phase of a pressure wave, where the density of the medium decreases I guess that might be possible but it raises a number of questions. (The osculations would be both larger than our universe and longer than its lifetime so far and also of an odd waveform to deal with our big bang.)

      1. The elastic liquid filled balloon could be better visualized if you consider although gravity defines the boundaries it is not strong enough at this scale (space) to restore (re; big bang) and maintain symmetry. So, because of irregular densities of the energy concentrations, broad band oscillations will arise, stretching and expanding (ballooning) is some places and compressing in others. And I believe you will find the galaxies and filaments on transitions regions where the stretching of space is minimal hence more stable for maintaining matter (galaxies).

        Of course, if an observer goes far enough away he will see a very large spherical balloon and the surface waving.

        Interesting part of this analogy is what happens when space stretches so much that a region(s) are created where the vacuum drops below the ZPE level (if possible)? Will it repair itself or cause a cataclysmic destruction of the whole universe?

        1. The oscillations as you describe them are problematic; firstly the alrge scale structure of the universe does not show any sort of regularity as would be expected from being the result of waves of compression-rarifcation. It tends to be rather fractal in nature forming ‘knots’ and filaments’ whereas waves would tend to produce ‘bands’ and ‘islands’ (This can be seen when you shine light through the surface of a wavy pool; you will see stripes and bands and islands but never a spiderweb like pattern, no matter how complex the waves get.) This structure also arises naturally when we work with models of an expanding universe and gravity; the present rate of expansion large scale structures are quite stable.

          The large scale structure of the universe also shows no signs of moving, which would be expected if the oscillations were anything but standing waves; as far as we can tell galaxies formed pretty uniformly, waves would be expected to leave ‘fronts’ of galaxy formation and ‘backs’ of galaxies being torn apart. We would also be able to detect from the redshift of said galaxies the different speed of expanding space in the different areas. Indeed your model would violate a basic principle of cosmology, that the universe is pretty much the same everywhere.

  23. I happened across a statement that said primordial black holes from the outside would be as small as an atom however from the inside would seemingly appear as large as the observable universe? True?

    1. That is a rather strange statement; the limit as to how light and thus how small from the outside black holes can be (at some point they disintegrate.) is not pinned down as far as I know, but from the inside (IF BHs can in fact be viewed from the inside, see the recent ‘firewall’ controversy) they look no different from ordinary space. You cannot tell you have passed the event horizon though gravitational effects cause some interesting phenomena.

      Possibly the statement refers to the ‘infinite gravitational well’ from which nothing can escape or the way space behaves in a BH but in terms of appearing to be a 93 billion light year expanse of relatively flat space, no sir.

  24. Ian – if dark matter were primordial black holes, then for some mass ranges they would exchange energy with ordinary matter (through purely gravitational interactions) as they plunge through the disk. In principle, that “cools” the dark matter (in the sense of reducing the random velocities). However it also “heats” the ordinary matter, making gas hotter (which is fine, as the gas can radiate) and the stellar disk thicker. Since even the oldest disk stars are still orbiting in a relatively thin disk, there are quite good limits on how much dynamical heating there can have been, and hence on how much dark matter can be in the form of black holes in some mass ranges. As with most astrophysical constraints, the exact numbers are subject to uncertainty.

  25. I have just received reports that there was a gamma ray burst in M31 today about 5:00 PM EDT. Don’t know of any reports of other wavelengths / methods (but I bet people will check their neutrino detectors tonight, and I hope someone has a gravitational wave detector up). The hashtag for this is #GRBm31

  26. On the subject of PBHs, I’d also be interested in the argument that explains why they don’t end up in a flat disk the way normal matter does in galaxies. I couldn’t find the explanation anywhere.

    Thanks you for the report on the talks, very interesting as usual. Your blog sits at the top of my list,

    1. Objects end up in a flat disk only if they can radiate energy and angular momentum sufficiently quickly. Gas made from atoms will do this, by radiating photons; dark matter, being dark, can’t, and that includes primordial black holes. [Although it is possible that a subcomponent of the dark matter can radiate, by emitting some new type of massless particle, and form a second disk, perhaps not quite parallel to the visible disk. The people who have recently explored this idea are Jiji Fan, Lisa Randall and Matt Reece.]

      1. Thank you for the explanation. Except… this describes why they would spiral inward, but assembling into a flat disk is a pure dynamical effect as soon as you have 3 or more gravitionally interacting bodies. I’m afraid I disagree with this being the reason (and I can’t believe I dare to say based on memory of high-school teaching!)

        1. The formation of a disk, and of spiral bands, is an extremely complex subject, not something you can figure out with high-school physics, or even college physics. It’s very much graduate level. See this from one of the experts, written in 2002: http://ned.ipac.caltech.edu/level5/Sept02/Silk/frames.html . Probably one of my readers can get you something more up-to-date. My point was that a critical ingredient in disk formation is radiation of energy and angular momentum; dark matter that cannot radiate a substantial amount of energy cannot form a disk, whether it is particles or black holes. [And no, Hawking radiation is far too weak to assist in this process.] I agree that my point does not explain why a disk forms; it merely provides a necessary (but not sufficient) condition.

          1. Unless I have misunderstood your reference, one way around the problem of dark matter not being able to radiate could involve collisional accretion, the dark matter exchanging energy with normal matter through collisions, the latter doing the radiating. I realize that in itself is not sufficient to explain disk formation, but perhaps it might get around the issue of dark matter being unable to radiate.

            1. If collisions were that common and effective, then we’d have discovered dark matter directly long ago, through its collisions with atoms in detectors much simpler and smaller than the ones we currently use. The whole point is that dark matter barely interacts with ordinary matter, neither colliding with atoms and their constituents nor absorbing and emitting photons.

  27. @RLO – PBH have in my opinion been largely ruled out (as DM) by a combination of gravitational microlensing (which eliminates PBH more massive than the Earth or so – see http://adsabs.harvard.edu/abs/2013PhRvL.111r1302G) and consideration of the effects of capturing smaller PBH in neutron stars and other objects (see http://arxiv.org/abs/1401.3025) (I think that the PBH capture idea can be extended to smaller objects, which would deal with the objections in http://arxiv.org/abs/1402.4671.)

    1. M.R.S. Hawkins has presented an excellent case for PBHs as dark matter candidates. See: http://arxiv.org/abs/1106.3875 .

      The main problem with the PBH candidacy is that it is not the answer that is wanted, so the majority do their best to shoot it down with various theoretical arguments.

      Microlensing experiments have discovered a very large population of unidentified stellar and planetary-mass objects that are most easily explained in terms of PBHs. Critics counter that they could only make up 20% of the dark matter, based on several theoretical assumptions. Apparently 100 billion objects does not impress them.

      1. “The main problem with the PBH candidacy is that it is not the answer that is wanted”

        That’s simply not correct.

        Moreover, you are ignoring the recent work (from 2013-2014) that has undermined the case that is made in the paper that you quote (from 2011). I think your knowledge is out of date.

        1. Indeed; it is simply not correct. Indeed, RLO’s knowledge is out of date. Hawkins’s original idea was briliant, one reason being that it made very concrete predictions. But since some of these were falsified, his idea is wrong. That is how science works. I even had something to do with this. Of course, if one reads only Hawkins’s papers and those he cites, one doesn’t get the full picture. Normally, when one writes a paper, one should respond to, or at least acknowledge, criticism in the literature, even if one does not agree with it. Ignoring it reflects badly only on the person doing the ignoring.

        2. If you look at discussions of the dark matter problem in popular science literature (Science, Nature, etc.) or in professional journals, you will see that the discussion is about 99% about various speculative and poorly defined (uncertain masses, etc.) particle DM candidates.

          The physics community is virtually sure the DM is some form of WIMPy particle.

          You vastly underestimate the bias against astrophysical DM candidates and the weakness of the theoretical arguments and assumptions that provide a cover for this bias.

          I do not think the problem is me being out of date, but is due to the theoretical physics community once again being “… wrong, but never in doubt”.

          1. Again, I don’t see the bias you see being as strong as you believe. The *particle physics* community seems largely to assume dark matter is a particle. I don’t see that in wider circles; and in any case, I don’t assume it. What I do see is papers that show that certain types of things are impossible for dark matter, including large classes of primordial black holes.

            It’s kind of slanderous to accuse the theoretical physics community of being wrong but never in doubt. Do you really want to insult everyone in this community? This is not a good way to encourage people to pay attention to you.

          2. “I do not think the problem is me being out of date, but is due to the theoretical physics community once again being “… wrong, but never in doubt”.”

            And of this, you have no doubt?

          3. @RLO – I think you are simply wrong in your conclusions about the physics / astronomy community. To me, the most important and most fundamental thing in dealing with any scientific problem is, do you have theories that make testable predictions? There is no short of testable predictions from WIMPs, or from PBH, or from other DM ideas, and lots of thinking about ways to test them. In my opinion, things do not look good for PBH as dark matter, and that has nothing to do with the current fondness for WIMPs as a DM explanation, but with observational problems with PBH, and this is not being driven by the WIMP community, much less by theoretical physics.

            Now, if you want to argue that too much money is being spent testing WIMPs, and some of it would be better spent testing DM hypothesis X, then that is a different matter and certainly worthy of discussion.

            I was at the Sackler debates by the way, and I can assure you that there were a wide range of opinions present. It was in my opinion a really first-rate meeting, and very informative on a host of topics.

          4. 1. I am not trying to “encourage people to pay attention to [me]”.
            2. Nature’s verdict, via observations, will eventually be forthcoming. Then we will see whose reasoning was the most scientifically sound.

            1. 1. If you are not trying to encourage people to pay attention to you, then why are you making such a big deal about this in the first place? This is disingenuous.

              2. No, we will not see whose reasoning was more sound. One’s reasoning can be perfectly sound, and yet nature may disagree with it; similarly, one can apply bad reasoning and yet guess what nature is doing. All we will learn is about nature, not about people. And frankly, in this context, that’s all I care about.

          5. The dark matter enigma has been around for several decades and little real progress has been made. Maybe it is time for new ideas, rather than blindly insisting that no-show WIMPs are the only path worth pursuing.

            Science is supposed to be open-minded to new ideas, and skeptical of all inadequately tested assumptions. Do you have a problem with that?

            1. You may have noticed that there are dozens and dozens of papers since 2008 on non-WIMP dark matter. Maybe you haven’t been reading the archive. When you say “Maybe it is time for new ideas, rather than blindly insisting that no-show WIMPs are the only path worth pursuing…Science is supposed to be open-minded to new ideas, and skeptical of all inadequately tested assumptions. Do you have a problem with that? “, all I can say is that you are revealing a deep-seated ignorance.

      2. And I think that you are revealing the fact that you do not like your authority or the absolute authority of the standard paradigm questioned.

        So you feel the need to insult the impudent offender and imply that he is out of touch and/or out of his depth.

        I follow everything published on the topic of dark matter because I have a very special interest in that topic. If we ever want to solve the dark matter enigma, it will take old school science, not new age pseudo-science.

        1. It’s up to you if you want to live in your own world of bile.

          Note that on this very page, the issue of Zhitnitsky’s suggestion regarding dark matter is being discussed. This is not about WIMPs. Do you see me shutting down this discussion? What is the matter with you?

          1. Apparently the matter is simply that I fundamentally disagree with you about bias in assumptions about the best course for dark matter research, and you cannot accept that there are alternative ways to assess the situation in dark matter research.

            Your responses are mostly insults and anecdotal reasoning. So what’s your problem?

            1. My problem is simply that sometimes I get commenters who are so locked into a single issue that they can’t hear what others say or think about anything except the point they’re trying to make. You made your point, and insulted everyone in the field in the process.

          2. And my problem is that I think dark matter research is infected by an obvious bias that insists that the dark matter must be some form of subatomic particle. PBHs are just one alternative. There are many others.

            That is a very general issue, not some narrow point.

            It seems to me that if you question this bias the masters of the universe stamp their little feet and get all red in the face.

            Perhaps they are over-reacting to some much needed scientific skepticism?

            1. I don’t agree with you that this bias is so severe. I completely agree with you that there are many alternatives, and so do many of my colleagues, as I know from direct discussions with them. And I’ve said this repeatedly on this website.

          3. So we agree to disagree about the degree of bias for particle dark matter and against astrophysical dark matter. Let’s leave it at that.

            I really liked your discussion of the knowns/unknowns of the standard Big Bang cosmology, and I recommended that others carefully read it at other venues like sci.astro.research.

          4. You can agree to disagree, but given the existence of non-WIMP hypothesis coverage *right here*, it’s clear this is not just a matter of disagreeing with another’s opinion, but disagreeing with reality in favor of personal opinion.

  28. Thank you for a brief report this conference. So, no news. No annihilation, no direct detection and no production to report. What are they WIMPs? Perhaps super-WIMPs, some supersymmetric WIMP-less framework?
    Take a child out in the Atacama desert on a moonless night for star-gazing ask them to look up and tell you what they see. They’ll say, ” It’s mostly dark.”
    Take heart. Children were able to see that the continents fit together like a jigsaw puzzle long before tectonic plates and continental drift were postulated.
    I maintain Dark matter/energy are almost perfectly analogous for human ignorance and our wasted potential.
    To state it will or should be detected in a finite period is hubris. Be careful of that.

  29. The gravitational force attracting the matter, causing concentration of the matter in a small space and leaving much space with low matter concentration: dark matter and energy. There is an asymmetry between the mass of the electric charges, for example proton and electron, can understood by the asymmetrical Planck Distribution Law. This temperature dependent energy distribution is asymmetric around the maximum intensity, where the annihilation of matter and antimatter is a high probability event. The asymmetric sides are creating different frequencies of electromagnetic radiations being in the same intensity level and compensating each other. One of these compensating ratios is the electron – proton mass ratio. The lower energy side has no compensating intensity level, it is the dark energy and the corresponding matter is the dark matter. https://www.academia.edu/6410478/Dark_Matter_and_Energy

    1. Seems a little unfair. You mension the mass ratio between electron and proton, not the best example. One is a particle, the other a system of 3 particles. How about between the three neutrinos. The mass ratios are EXACTLY 1:2:3, with a total mass of about 0.23 ev ? How does that fix your data ?

        1. Thanks for your help Matt. I know you will not be surprised by what you can find when double checking ones work.

          1. Well double checked; the neutrinos masses are .04, .08, and .12ev. If you feel there is a better answers , please tell us. And I should not have said 3 particles but 3 ferimons, plus about 1,000,000 bosons.

  30. My understanding is that the dark matter galactic model is based on non-relativistic Newton’s law of gravity. Is it possible that the answer may be that the dark matter particles are of masses and energies in the TeV range or higher and since the cross sections fall rapidly with energy, the present methods will never detect them?

    1. No, that’s not the case. Dark matter is included in the fully general-relativistic model of cosmology extending back to the very early period of the universe.

      But that is irrelevant to your question. Yes, dark matter may be made of particles whose masses are in ranges (either too small or too large) that make them very difficult to detect with current methods. In the case of very heavy particles (TeV to trillions of TeV) the problem is not just that their cross-sections are small but that they will be very rare; we know roughly how much dark matter there is [if it’s really there] BY MASS, so when you translate that into the NUMBER of particles, that number goes down as the mass of the particles goes up.

      1. Thanks. Then I take it that they have indeed considered motion of stars around galactic centers and galactic rotation with GR along with dark matter. Then MOND is a very poor argument. Previously I thought that the reason why dark matter was in cosmological models was just to make Omega (tot) =1. Of course if both galactic motion and cosmology need same kind of dark matter, it would make the case for dark matter much stronger.

        1. Dark matter was never introduced to make Omega(total)=1; in fact, dark energy is what accomplishes this. Moreover, Omega=1 isn’t something that we theorize; it is something that we measure, today, to be very close to 1. So we’re not adding dark energy in by hand; we’re accepting what nature says about Omega, and about how the universe’s expansion is accelerating, which is again something that we measure.

          As for dark matter, not only motion of stars in galaxies but also motion of galaxies in clusters; gravitational lensing of objects by objects in front of them; the patterns in the cosmic microwave background; the fact that galaxies form at all — there are numerous lines of argument that all agree about the amount of dark matter in the universe.

          1. Agreed. There are strong arguments for existence of dark matter. Now the situation may be developing like supersymmetry. Most theorists want it but if experiments cannot find it then what? I suppose there are not many believable models without dark matter.

      2. You offer a mention of cosmological models to counter kashyap vasavada’s statement “My understanding is that the dark matter _galactic_ model is based on non-relativistic Newton’s law of gravity.”

        As I understand, kashyap vasavada is correct in that non-relativistic models were and are usually still used to infer the existence of _galactic_ dark matter. In general terms, the requirement for galactic dark matter is justified by the discrepancy with expectations that rotational velocity should diminish as a function of radial distance.

        Very interestingly, a recent paper – http://arxiv.org/abs/1401.7063 – identifies three “Gravitational anomalies signaling the breakdown of classical gravity”. I’m specifically very interested in section II, which describes the flat orbital velocity : distance relation for hundreds of low-mass, widely separated (low energy) binary star systems in our galactic neighborhood – primarily because of its fundamental nature.

        This simple phenomenon seems to correspond to the flat rotation curve of spiral galaxies. While the authors view these anomalies as evidence against both Newton’s gravitation and general relativity – requiring their modification, IMO they do not thoroughly consider potential solutions using GR.

        Of course, GR is distinguished from Newtonian gravity in accounting for the amplification of effects high-energy conditions (including the proximity curvature of light by the Sun). It occurs to me that the might be a yet unidentified low-energy condition that also does not comply with the Newtonian inverse square rule.

        In particular, it seems that Newtonian gravity implicitly aggregates the masses of two bodies and considers that the gravitational interaction occurs at the limit of the separation distance between the two bodies.

        While I can’t evaluate, it seems that in GR two low-mass stellar objects would each produce their own fields of curved spacetime – and that the gravitational interaction physically occurs at the boundary intersection of the two fields. As such, the (circular) geometric area of intersection/interaction between the two fields would _increase_ with separation distance, even as the strength of the two fields diminish. In this way, the gravitational interaction between two substantial (spherical) stellar bodies might stabilize at some distance – as observed.

        At any rate, I would like to challenge anyone to construct a potential dark matter configuration in our own galactic neighborhood that could produce the flat velocity : separation distance relation observed for hundreds of low mass, widely separated binary stellar systems…

  31. One hopes that microlensing observations may offer the guidance on primordial black holes as dark matter. There is more physical evidence for this PBH candidacy than for all particle candidates combined.

  32. We should include MOG by Moffat who uses GR as a basis and increases gravity as a function of distance. Moffat claims to be better than MOND, GR or any other theory. Neither explain why. There is also LSG, which does give a reason, a rather simple one, but requires gravitons ot travel FTL. There are about 20 different theories, hard to find the RIGHT one, half use dark matter, half don’t.

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