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Dark Matter Puzzle Solved?

  1. Nov 9, 2004 #1

    Chronos

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    Authors propose solution to dark matter and alternative to MOND.
    Higher Order Curvature Theories of Gravity Matched with Observations: a Bridge Between Dark Energy and Dark Matter Problems
    http://www.arxiv.org/abs/astro-ph/0411114

    Higher order curvature gravity has recently received a lot of attention due to the fact that it gives rise to cosmological models which seem capable of solving dark energy and quintessence issues without using "ad hoc" scalar fields. Such an approach is naturally related to fundamental theories of quantum gravity which predict higher order terms for loop expansions of quantum fields in curved spacetimes. In this framework, we obtain a class of cosmological solutions which are fitted against cosmological data. We reproduce reliable models able to fit high redshift supernovae and WMAP observations. The age of the universe and other cosmological parameters are recovered in this context. Furthermore, in the weak field limit, we obtain gravitational potentials which differ from the Newtonian one because of repulsive corrections increasing with distance. We evaluate the rotation curve of our Galaxy and compare it with the observed data in order to test the viability of these theories and to estimate the scale-length of the correction. It is remarkable that the Milky Way rotation curve is well fitted without the need of any dark matter halo and similar results hold also for other galaxies
     
    Last edited: Nov 9, 2004
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  3. Nov 9, 2004 #2

    turbo

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    The dark matter puzzle is not yet solved, but it is encouraging to see progress, or at least questions tending in the right direction. I am a bit skeptical of the supposedly great "fit" of the Milky Way's rotational curve, given the large error bars in the diagram.

    You will notice that in the introduction the authors mention that if we attribute the cosmological constant to the energy of the vacuum fields, the CC will be 120 OOM too small. This is a common misconception. The problem arises when we calculate the absolute energy density of the quantum vacuum fields relative to a theoretical pure vacuum, which cannot exist in our universe. The quantum ZPE field is the ground state of our universe, so the theoretical "absolute" energy of these fields is irrelevant. In our universe, we can only measure and exploit differences in energy levels. If gravity is to be combined with the other fundamental forces, the quantum folks have got to start calculating vacuum field strengths relative to our universe's ground state, not relative to a theoretical empty frame. This will solve the "120 OOM" problem immediately, and will allow the ZPE fields to be incorporated into cosmology with respect to inertia and gravity without these really large errors. For those that might be just skimming this post, 120 OOM means 120 Orders of Magnitude, which is equivalent to multiplying the force of the cosmological constant by 10 to the 120th power. That's a pretty big number, and it's giving some folks fits.
     
  4. Nov 10, 2004 #3

    Garth

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    If the answer is so blindingly obvious why is it giving some folks (some of the best minds in the business) fits?

    Chronos - Are "Higher Order Curvature Theories of Gravity" readily testable and falsifiable?

    Garth
     
  5. Nov 10, 2004 #4

    turbo

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    I do not mean to be flippant, but it is getting a bit tedious hearing about the 120 OOM "too energetic" vacuum energy.

    Let's use an analogy in electronics: take a simple circuit (like an old guitar amplifier or a radio) that incorporates capacitors to block the flow of DC. Introduce an alternating current of 120 volts, and the amplifier functions properly. Now introduce a DC potential to that circuit, so that the baseline voltage around which the 120V AC oscillates is +5 V DC, +10 V DC, +20 V DC, etc. The amplifier continues to function normally, and unless you measure that DC potential to ground, you would never know that it is there. The same is true for the ZPE fields in our universe. They are the ground state of our universe. Energy fluctuations higher or lower than that ground state can be measured and exploited, but without access to a "true" vacuum (which cannot exist in our universe), the absolute energy of the ZPE fields cannot be expressed, measured, exploited, etc.

    There are a couple of problems contributing to this "120 OOM" situation. One is that the quantum theorists express the ZPE energy density in terms of "absolute" energy relative to a theoretical pure empty reference frame, which cannot exist in our universe. Another is that some cosmologists plug these energy numbers into their calculations, as if the ground state energy does not really exist as the ground state. Once it is aknowledged that the ZPE fields are pervasive, the theoretical "absolute" energy density of those fields needs to be zeroed out. Fluctuations above and below that ground state can be sensed and measured, but the ground state energy itself cannot.
     
  6. Nov 10, 2004 #5
    Hi Turbo-1

    Could you elaborate on the reasoning about why a theoretical pure empty reference frame cannot exist in our universe? Is it possible that you mean to say that such a reference frame cannot be measured in our universe? I am asking because I have been thinking theoretically that at extremely short distances and times (near Planck length and time) there may be a condition similar to Mach space, empty of any matter or field. This would be due to the fact that nothing material could fit into such a small space, and nothing energetic could take place in such a short time. Also, in such a small space and time, no information about neighboring states could flow in or out of the locality. So, if I have it correctly, these extremely tiny regions would constitute the equivalent of an absolute vacuum state.

    This would be a trivial solution, except that I suspect that there may be very many such states permeating our ordinary space, and that such states are connected geometrically. If so, while we may not be able to measure any one of them, it could be possible to measure them in agglomeration. Essentially, if there is a fabric of spacetime, which I believe is not considered too outlandish an idea, these vacuum states would be the spaces between the threads in the fabric.

    Any thoughts on this?

    Thanks,

    nc
     
  7. Nov 10, 2004 #6

    turbo

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    Hi Nightcleaner. According to quantum theorists, the ZPE fields of the "vacuum" are the ground state of our universe. In other words, in "empty" space, at zero degrees Kelvin, (the definition of zero point) there is a sea of virtual particle/anti-particle pairs spontaneously emerging and self-annihilating. We can create a field slightly under the energy density of the ZPE field in a Casimir-force test device by restricting the emergence of some frequencies of the ZPE spectrum. This is done by putting parallel conducting plates VERY close to one another, so that some of the virtual pairs cannot form. Apart from special situations such as this, the ZPE field is all-pervasive. Intuitively, I think your concept of scales (space and time) so tiny that the virtual pairs cannot form is interesting. Their applicability to the unification of gravity to the other fundamental forces will per force have to take into consideration the laws of our observable universe, though, and this is where the 120 OOM disconnect comes in. We apparently live in a universe with a VERY energetic ground state (compared to a theoretically empty reference frame), and we experience energy differentials in relation to that ground state.

    It may indeed be a trivial solution, but what if can be extrapolated to something more general? The people working on quantum gravity are indeed studying the "fabric of spacetime" and speak of spin foam and other such concepts.
     
  8. Nov 10, 2004 #7

    GENIERE

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    I'm curious why you emphasize "VERY close". It would seem to me the force is not restricted to short wavelengths, simply easier to measure. Plates in close proximity exclude the longer wavelengths thereby adding to the Casimir pressure whereas macro spacing does not exclude the longer wavelengths thus they cannot add to the effect.
     
  9. Nov 11, 2004 #8

    Chronos

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    Good question Garth. I took that was the main point of this paper. It is a followup to a previous paper by the same group where the concept was proposed:

    Can higher order curvature theories explain rotation curves of galaxies?
    http://www.arxiv.org/abs/gr-qc/0404114

    In the more recent paper they explain in particular how they tested those predictions by plotting galactic rotation curves.

    I am a real sucker for stuff like that... frame a theory that makes a prediction, suggest a way to test it and then actually follow up. It would be interesting to see some independent corroborations. None have yet materialized.
     
  10. Nov 11, 2004 #9

    Chronos

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    The reason it is considered too energetic is because it results in an absurdly high cosmological constant. My reasoning for making this assertion is found here:
    http://super.colorado.edu/~michaele/Lambda/phys.html
    There is nothing theoretical about the relationship between a field with energy density and a field that has no energy density. Whether a zero energy field actually exists is not relevant.
    Huh? Symbolic logic suggests that assertion may be flawed.
    See above. If the ground state energy itself cannot be sensed, how might you go about sensing and measuring fluctuations relative to it?
     
    Last edited: Nov 11, 2004
  11. Nov 11, 2004 #10

    turbo

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    The point that I am making, and have made countless times is that this energy level is the ground-state of our universe. Are you familiar with basic electronics? If so, imagine that you are in a Faraday cage with some basic electronic circuits. You have NO access to an outside ground, only your local ground, which is the frame of the Faraday cage. As you are testing your electronic devices, someone outside the cage starts putting a DC potential on the cage. You, the cage, and everything in it is now at a potential of 500V DC above the ground of the lab. You are inside the cage with your circuits and you have no access to the lab's ground - now way to test or measure the potential of the cage with respect to the lab's electrical ground. Your circuits are working perfectly, you feel fine, and you have NO idea (and no way to discover) that the Faraday cage and everything in it are riding +500V DC above the lab's ground. We are in an analogous state in our universe. Quantum theorists have determined that the ZPE fields contain huge amounts of energy relative to a theoretical empty frame, but without access to such a frame, that "absolute" energy level cannot be expressed or measured. Theoretically, that energy level is great, but in our universe it is the ground state - the minimum energy level at which "empty space" can exist.

    A field with no energy density is entirely theoretical, since the ZPE field energy is the ground state of our universe. Combining quantum theory with gravitation will require the incorporation of this concept. Moving from the theoretical (quantum theory) to the practical (GR, gravitation) will require that assumptions in each field of study be reconciled with one another. Read the papers of the Loop Quantum Gravity folks, and you will see how they are trying to relate quantum theory to the mechanics (form, structure, energy) of the GR universe.

    We can measure the Casimir Force, which is a fluctuation below the ground state of the ZPE field. Case closed.

    If the ZPE fields are polarized in the presence of matter, as I surmise, we can probably also measure the flux density of those fields with a sufficiently sensitive orbiting Casimir-type experiment.
     
  12. Nov 11, 2004 #11

    Garth

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    Is not the problem with the Faraday cage analogy that in the case of energy, and unlike electric potental even though classically only changes of energy level can be measured, in GR energy has a mass equivalent with its corresponding gravitational field, and this ought to be measurable?
    Garth
     
  13. Nov 11, 2004 #12
     
  14. Nov 11, 2004 #13

    turbo

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    Interesting question, although I have to ask "against what standard can we measure the mass equivalence of the quantuum vacuum?" Quantum theorists would say with some justification "let's extrapolate down to a frame devoid of energy and calculate the absolute energy from there. That gives us tremendous absolute energy, but in real-world (GR) terms it gives us exactly zero energy differential relative to our universal ground state.

    That puts us back in the Faraday cage situation with no access to the theoretical no-energy reference frame. Everything that we measure in classical physics is measured against some standard. Since the energy of the quantum vacuum is the ground state of our universe, we may have to
    reconcile ourselves to the fact that the mass-equivalence of the ZPE field (zero-degree Kelvin "empty" space, undistorted by mass) may be zero, or at least undistinguishable from zero in our reference frame. The quantum gravity folks will have to wrestle with this one.
     
  15. Nov 11, 2004 #14

    ohwilleke

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    A number of others have pursued similar appoaches. For example Bekestein created, this summer, a fairly rigorous relativistic Modified Newtonian Dyanamics which has been tested in the non-relativistic area against the dynamics of hundreds of galaxies eliminating the need for dark matter. See here: http://arxiv.org/abs/astro-ph/0403694 Developing an idea first formulated in rudimentary ways in 1983 by Milgrom: http://adsabs.harvard.edu/cgi-bin/n...J...270..365M&db_key=AST&high=32f602678018216 and to a great extent advocated for by Sanders and McGaugh in publications like this one: http://arxiv.org/abs/astro-ph/0204521 But, the cosmological implications have only been sketched out. One corollary of MOND is that very distant masses have far stronger field effects on each other than in Newtonian dynamics, because at great distances MOND gravity falls off at 1/r rather than 1/r^2, which have largely been acknowledged but not rigorously examined to date. Eliminating dark matter also dramatically reduces the total amount of "stuff" to be accounted for in relativistic cosomology equations now used.

    The dark energy fraction (currently 0.7) is very sensitive to the Hubble constant. A 30% shift from the 70s for the Hubble Constant as implied by the HST study to the 40s would end the need for dark energy at all according to Shanks: http://xxx.lanl.gov/abs/astro-ph/0401409 and Blankard et al: http://arxiv.org/PS_cache/astro-ph/pdf/0304/0304237.pdf and lensing studies show Hubble Constant values closer to the 50s: http://www-utap.phys.s.u-tokyo.ac.jp/~oguri/files/ppt/iau_map.pdf while Tully-Fisher distances may also be as much as 27% high according this study: http://xxx.lanl.gov/PS_cache/astro-ph/pdf/0208/0208237.pdf It isn't unthinkable that dark energy is similarly sensitive to other less studied factors in cosmology equations, such a weak field MOND effects or a change in the total amount of gravity outstanding as the author in the originally cited article seem to think.

    Cadoni has made another effort here: http://arxiv.org/abs/gr-qc/0312054 but it violates the equivalence principle. Sanders also made a flawed prior effort called phase coupled gravity: http://adsabs.harvard.edu/cgi-bin/n...RAS.235..105S&db_key=AST&high=32f602678022152

    Periwal here: http://xxx.lanl.gov/PS_cache/astro-ph/pdf/9906/9906253.pdf and Deur here: http://arxiv.org/abs/astro-ph/?0309474 have proposed MOND as a consequence of quantum gravity, as so Consoli and Siringo: http://xxx.lanl.gov/abs/hep-ph/9910372
     
  16. Nov 11, 2004 #15

    ohwilleke

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    The physical evidence for dark energy independent of cosmological considerations see: http://xxx.lanl.gov/abs/astro-ph/0307335 is the biggest barrier, of course, to eliminating dark energy entirely from cosmology.
     
  17. Nov 11, 2004 #16

    marcus

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    Is there some logical connection between DM and DE? or, since i guess there is, could you sketch out the connection please?

    this article you cite is about physical evidence for DE.

    the Bekenstein article you flagged for us earlier is, if I understand correctly, about a nice MOND model that does away for the need for DM.

    If we do away with the need for DM to explain galaxy rotation curves and to explain how clusters of galaxies hang together, then we still have the accelerating expansion of the universe-----and its apparent (near) flatness.

    So it seems we would still need a postive cosmological constant, which I picture as a slight built-in curvature that the universe just has without the need for matter to cause it----or some corresponding amount of dark energy---to balance the books.

    does Bekenstein obviate DE too? sorry if I am not getting it.

    just to keep the links handy, there was this paper in October about possible ways to avoid the need for Dark Energy----with some majorleague co-authors:

    Sean M. Carroll, Antonio De Felice, Vikram Duvvuri, Damien A. Easson, Mark Trodden, Michael S. Turner
    The Cosmology of Generalized Modified Gravity Models
    27 pages, 7 figures
    http://arxiv.org/abs/astro-ph/0410031

    "We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models, examining the possibilities for cosmic acceleration and other ultimate destinies. The models generically possess de Sitter space as an unstable solution and exhibit an interesting set of attractor solutions which, in some cases, provide alternatives to dark energy models."

    cant comment, at least for now. but my feeling is that we might be seeing the germs of some kind of simplification which can dispense with either DM or DE, or both. Might involve a new physical constant.
     
    Last edited: Nov 11, 2004
  18. Nov 11, 2004 #17

    Garth

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    The above paper makes the following statement "Assuming a flat universe, our preliminary detection of the ISW effect provides independent physical evidence for the existence of dark energy." Does the assumption of a flat universe really amount to an assumption that Omega total = 1? A non-standard gravitational theory would not necessarily make this connection.

    There is also another view of the same correlation in the data, "Differentiating between Modified Gravity and Dark Energy"
    http://xxx.lanl.gov/abs/astro-ph/0307034

    Garth
     
  19. Nov 11, 2004 #18

    ohwilleke

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    Most cosmology models start with the assumption that Bayronic matter plus dark matter plus dark energy equals the total sum of all stuff in the universe. The amount of dark energy as a proportion of that in turn drives what the cosmological constant must be. Ditch the DM and you do a number of things.

    1. You may change the amount of dark energy needed to make the cosmological constant and the toal amount of mass-energy in the universe balance. This impacts, for example the matter-energy density of space which shows up in the p terms in Friedman's equations.
    2. You throw off a whole bunch of assumptions that form the basis for determining basic cosmological constants. For example, one important set of assumptions flows from the assumption that CBM background radiation profiles are a product of cold dark matter. If you have a different model that produces the same CBM background radiation profile without cold dark matter, you fundamentally change the assumption used to place limits on permissible values like the cosmological constant (to which the dark energy fraction is sensitive) and the density of space. The chart on page 2 of this paper: http://arxiv.org/PS_cache/astro-ph/pdf/0403/0403064.pdf shows in full color how the cosmological constant and fraction of matter made of matter (Omega M) are related and shows quite vividly that the orange splotch which represents the permissible range based on CBM data is the biggest straight jacket on that result. Going from CDM to MOND both changes the shape of that straight jacket (this point 2) and pushes you to a different point on the Omega M axis (point 1 above).
    3. CDM basically says "Newtonian gravity applies", we have these "dynamics" and we see this "mass", where do I need to put more mass to make the number fit. Locally, these results should be the same. But, when you leave the localized system of say, a galaxy, the gravity from the CDM to make that localized system fit is going to fall off as /1R^2. But, in a MOND regime, you are giong to see that gravity outside the localized system fall off as 1/R.

    Consider this ill thought out, spur of the moment example. Suppose gravity has a very low force which induces an accelleration a its fringe with radius 1 unit. A hundred galactic radii out CDM says gravity is 0.0001a while MOND says that gravity is 0.01a. The effect is small, but it is non-zero. We know that in GR, gravity induces time dilation. If gravity in the middle of nowhere is 100-1000 times what was previously anticipated, this could produce a small effect, but one that would be measurable, over long distances. If that happened, it would intensify redshifts without breaking the harmony between redshifts and time dilation which we now observe. Screw up redshifts and you screw up Hubble's constant, driving it down. Drive Hubble's constant down 30%, and you don't need dark energy any more. Moreover, maybe with points 1 and 2 above considered, maybe now you only need to drive down Hubble's constant by 15% to make DE go away.

    Obviously, if I had it all worked out, I'd write a paper and publish it, but the gist of the notion is that CDM assumptions are deeply relied upon for a foundation of our current cosmological estimates and constant calculations.

    This is just to point out that as nice as it would be to get rid of DE, that if you replicate studies like that one where DE is shown to be "real" then no matter how good a theory you can come up with to eliminate DE, that theory will be wrong. Of course, maybe physical evidence of DE is really just physical evidence for something else (like distorted gravity) that looks like DE.

    Bekenstein actually puts a cosmological constant at the canonical value in his model. But, Bekenstein isn't a cosmologist, he's a phenomenolical astronomer and isn't a natural at thinking through the subtler implications of his own theory. I was alluding to Carroll's article and similar articles (I believe Caroll actually mentions relativistic version of Milgrom's theory), to suggest that there may be subtle effects inducing curvature in a Caroll like analysis that flows from a Bekenstein theory which Bekenstein didn't catch but which would eliminate the need for DE.

    Yup. I think that it is quite likely that some combination of factors are going to return us to a no DM, no DE understanding of the world, which FWIW, also takes lots of pressure of the accellerator guys to discover new stable particles that can fit the bill of DM, and finely tuned non-zero vacuum energy to explain DE. Non-Bayronic means you have to come up with yucky stuff like Gondolo describes in this article: http://arxiv.org/PS_cache/astro-ph/pdf/0403/0403064.pdf (WIMPZILLAs et al), and I'm not sure CDM people have really come to terms with just how radical a proposal that would be.
     
    Last edited: Nov 11, 2004
  20. Nov 11, 2004 #19

    turbo

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    I rather like Cadoni's paper for several reasons, not the least of which is that he proposes the breaking of the equivalence principle. If polarized ZPE fields are the medium through which gravitational interaction is mediated, then the strict equivalence of gravitational mass and inertial mass must be broken. The last paragraph on page 5, rolling into page 6 is a very cogent description of the effects that I expect to result from ZPE-field gravitation. He says that this model is moving toward a Machian description of gravitational interaction. I believe that he is on the right track, but that in this Machian space, inertia is conferred not by acceleration relative to the entire universe (action at a distance) but by acceleration relative to the local ground state of the universe - the ZPE fields. Gravitation is also conferred by the interaction of mass with the local (polarized) ZPE field, and the polarized field is self-attractive and self-polarizing to an extent ("self coupling" in Cadoni's words.)

     
    Last edited: Nov 11, 2004
  21. Nov 11, 2004 #20

    ohwilleke

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    True, although a non-standard gravity close enough to GR to pass in observed circumstances would probably come close.

    The claim made that the conclusions he reaches apply to any modified gravity that follows Birkhoff's law (i.e. center of gravity effects are preserved) seems overreaching. After all, suppose that I use plain old GR and make the modification that a gravitation related constant varies over time according to some function F. It is a modification of gravity. By definition, it follows Birkhoff's law. Yet, such a prediction should be indistinguishable from current predictions for some forms of F. It isn't clear to me that simply by adding the contraint that the modification F eliminates the need for DE that you necessarily get the results suggested.
     
    Last edited: Nov 11, 2004
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