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Dark energy a furphy, says new paper

  1. Dec 28, 2007 #1


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    He makes some interesting claims:
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  3. Dec 28, 2007 #2


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    Here are Wiltshire's preprints
    I believe the one he just published this week in PRL, that the newsletter mentions, is #4 on the list (Exact solution to the averaging problem in cosmology)
    The other one, about time, that was mentioned further down, is #5 on the list (Cosmic clocks, cosmic variance and cosmic averages). That's the one published in New Journal of Physics.

    Here at Cosmology Forum we have been watching with some interest for the past couple of years, as Wiltshire has repeatedly published papers arguing that by abandoning the Copernican principle and assuming a largescale uneven distribution of matter we can do away with the need for dark energy. My feeling is it is a drastic price to pay to get rid of something that may be required for other reasons which Wiltshire does not acknowledge.

    Kea, who used to post a lot at PF, often called attention to Wiltshire's ideas. She is a grad student at the same Kiwi university as Wiltshire, and knows him. He is a respected reputable cosmologist and is doing what scientists are supposed to do----explore alternatives.

    There are several drawbacks. One is that abandoning the assumption of uniformity gives too much freedom. If you assume largescale irregularity you can concoct pictures so as to make virtually ANYTHING happen. Cosmologists usually assume largescale uniformity (homogeneous isotropic universe---the Cosmological Principle).
    Those assumptions make it harder to fit model to data--there's less wiggle room to fudge, so it narrows the field of competing models----it gives you traction.

    It would be extremely inconvenient to give up the Cosmological Principle.

    Although, as Wiltshire points out, giving it up would let you EXPLAIN things, by freely imagining a wealth of different distributions of matter out beyond where we can see.

    That is one drawback---it would be like pouring oil on the road. Less traction. Harder to do science. But that is just a practical disadvantage.

    Another drawback is that Wiltshire sets the cosmological constant to zero. BUT SOME UPANDCOMING QUANTUM GRAVITY theories require a small positive cosmo constant.
    They don't put it just because they WANT it. The model forces there to be a Lambda and refuses to work without it.
    I am not talking about some finetune Lambda being needed to fit the data. I am saying Lambda just to work at all.
    Some of the leading QG contenders are like that. And also some of the newest arrivals.
    Without saying which is which, I will mention a few QG approaches
    Reuter QEG
    Loll CDT
    Pereira dS-GR (actually predicts the observed Lambda value in relation to matter density)
    Sorkin Causal Sets approach (also predicts a value)

    This is not to say that these QG approaches are right, but there seems to be an effective need for Lambda coming up in theories----in effect the theories are recognizing the cosmo constant and saying what it IS in their terms. Usually in these cases no particle or field is required, the effect of a small positive cosmological constant emerges from the theory.

    I guess you could say that some or all of these approaches ALSO do away with the need for "dark energy" (in the sense of a mysterious field or particle with negative pressure) but they do away with it WITHOUT HAVING TO REARRANGE MATTER OUT BEYOND THE HORIZON, the way Wiltshire does.

    Anyway, if anyone is curious about what Wiltshire just got published in Physical Review Letters, the preprint is on that ArXiv list
    Last edited: Dec 28, 2007
  4. Dec 28, 2007 #3
    The concept of the age of the universe being dependent on frame of reference seems quite solid to me, and you don't have to abandon the cosmological principle to embrace it. Due to time dilation in strong gravitational fields and in rapidly moving frames of reference, the age of the universe has to vary significantly, even within our observable universe with its lace-like stucture. I hope much discussion of the implications of our "universe of variable age" continues.
  5. Dec 29, 2007 #4


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    Yes that seems pretty straightforward. I haven't looked at his article about clock variation that was #5 on the list and published in New Journal of Physics. I mentioned it because it was referred to in the popular newsletter.

    AFAIK Wiltshire doesn't say anything new or controversial in that one. But he may, you'd have to actually look at it.

    What is commonly accepted is (what you say) that time varies a lot depending on where the clock is. Recession speed does not affect it. And the speeds that do have affect are typically LOW like a few hundred km/s. (a tenth of a percent of speed of light) That does not affect time very much. But depth in a gravitational field could-----you mention the lacey cobwebby structure. That may be all Wiltshire is talking about in the article, in which case it wouldn't be especially interesting.

    You might want to take a look at the article and see if he gets into more radical terrritory. He may apply his notion of extra irregular density to explain acceleration as a local effect. That additional irregularity (which is so far just conjectural) would have an even larger effect on differences in time. There might be some observable consequences of that---but I'm only guessing.

    Why not take a look at the Clocks paper? If Wiltshire's line of investigation interests you.
    Ooops! I see that it is highly controversial too. It is not just about the well-established fact about time being slowed by gravity-well depth. It is another place where he goes whole-hog and explains away the cosmological constant. Well you still might want to glance at it.
    Last edited: Dec 29, 2007
  6. Dec 29, 2007 #5
    SF, you may want to check out http://https://www.physicsforums.com/showthread.php?t=201702&page=4" [Broken] thread here on PF.

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  7. Jan 18, 2008 #6
    "The age of the universe also depends on where you're standing, as Wiltshire discovered in calculations published in the New Journal of Physics.

    The universe is 14.7 billion years old, a billion years older than the currently accepted age, from our galactic observation point.

    But it is more than 18 billion years old from an average location in a void."


    When I first read this, my first thought was, is it possible that there is an alien life form out there that is 3.7 billion years more advanced than us in evoltion and technology? My second thought is any life form that is reasonably similar to us would probably have to evolve on a planet that has the minimum mass to hold water on its surface and have an atmosphere. The gravitational field on such a planet would largely be determined by the mass of the planet and insignificantly affected by the location of the planet in a void or otherwise. If that is a correct assumption, then it is unlikely that is there is a massive body supporting life forms that have a head start of billions of years over us. Does that seem reasonable?
  8. Jan 19, 2008 #7
    Hi Kev,

    I haven't done much reading on the topic of which galaxies might have the highest propensity for intelligent life at the present time. But I think the bottom line answer is that while there's a lot of speculation, no one really knows.

    Obviously, only a very small percentage of all galaxies are located well inside voids, so their opportunity to develop a given number of planets with complex life is far, far less than for filament/wall galaxies. But a small percentage still includes a very large (and potentially infinite) number of stars, so there is lots of statistical room for something to happen, in some void somewhere.

    An earth-type planet will develop only in a star system that has a reasonably high (but not too high) level of metallicity. Can't build earth out of just hydrogen and helium. Moderately high metallicity typically requires the star to form in a relatively long-lived galaxy which has had (potentially multiple) generations of star birth and death, enabling metal elements to be created and distributed by supernovae. Stellar lifespans are believed to have been quite short in the early universe, as stars were very large but had little metal content.

    New generations of active stellar birth tend to occur in regions (such as an AGN, active galactic nuclus) that are disrupted by some pwerful influence, such as shockwaves from a nearby black hole consuming stars, or from mergers between galaxies, dwarf galaxies and globular clusters. The more matter there is in a particular region, the more frequently these events occur. So overdense local regions probably are much more active in stellar regeneration in general than underdense local regions.

    On the other hand, life as we know it is likely to be utterly obliterated in regions where powerful energetic events occur, such as gamma ray and xray emissions in relativistic jets near some black holes, which can extend far enough that they could potentially destroy all life in a nearby galaxy which is aligned with the axis of the jet.

    So, the odds suggest that development and continuation of complex life is most likely to occur in modestly overdense regions in which the structure has been relatively stable for many gigayears. Not surprisingly, our Milky way galaxy resides in what seems to have been a fairly quiet corner of the local region, in a small filament not inside any massive rich galactic cluster, but nearby (attached to) a large supercluster. And our Sun is in a region of our galaxy which is at a relatively safe distance from the energetic events occuring in the galactic nucleus, but still within a "sweet spot" of moderately high metallicity. As I understand it, the Milky Way galaxy is believed to have been a fairly stable structure for more than 10 Gy. It probably was formed by accretion of numerous smaller galaxies, and more recently has merged with some dwarf galaxies and globular clusters. But it is not believed to have merged with any other large galaxy (unlike Andromeda, which is believed to be the result of such a merger). And the level of perturbation in the past 5 Gy probably has not stirred up much energetic activity in the Milky Way's nucleus. It is estimated that the Milky Way will merge with Andromeda 2-4 gigayears in the future, and that collison may stir up some dangerous activity in our nucleus, or not. Other than that, the future looks reasonably quiet for the galaxy, which probably is good news for us. But then, we simply don't know enough to predict various events which might prove catastrophic. And of course an isolated disruptive event such as an errant asteroid or comet collision could occur in our solar system which could wipe out life on earth.

    To make a long story short, my (relatively uneducated) guess is that complex life is statistically far less likely to arise in a void galaxy, since I predict that metallicity would be slow to rise to a sufficient level, although according to Wiltshire they could be up to 5 Gy behind us in metalicity development, and yet still be "caught up" with us from an evolutionary perspective because of their faster clocks.

    Last edited: Jan 19, 2008
  9. Jan 19, 2008 #8
    Jon, that was a very nicely written informative post. Thanks ;)

    One small issue you did not address was the relative time dilation of a void compared to a cluster. I have not gone into the maths in great detail, but I imagine that a planet like ours in a galaxy similar to ours but in a vast void would not differ greatly in time rate. I have seen a formula for the proper time of an orbiting object that takes orbital velocity, the altitude and the mass of the object it is orbiting into account. The distribution of matter outside its orbit (void or dense) would not appear to make much difference and a difference in the region of 4 billion years seems difficult to justify. For example the difference in time rate between a particle in the most empty remote part of space and a particle on the surface of the earth would not be that great and vast majority of the difference would be due to the mass of the earth and very little due to the mass of our galaxy or our velocity around the galaxy. To put it into context, the figures Wiltshire mentions imply a time dilation factor of around 30% which is a huge amount and only experienced at distance of twice the Schwarzchild radius from a black hole or when moving at a relative velocity of 70% the speed of light.
  10. Jan 20, 2008 #9
    Hi Kev,

    Your point is excellent, and is correct as a description of gravitationally bound systems.

    Wiltshire's central thesis is that although the geometry of space within bound wall and filament systems is approximately flat, the geometry in large voids has significant negative (open) geometric curvature. This follows logically from the significant (relative) underdensity of matter within voids. Negative curvature means that there is very powerful quasilocal (anti-) gravitational energy within voids. He uses a version of the Einstein equations (called Buchert's equations) to calulate that this gravitational energy differential, as compared to bound walls and filaments, causes void clocks to run significantly faster.

    Wiltshire points out that our galaxy has been gravitationally stable for at least 10Gy, so there has been that much time for void clocks to continue diverging from our local clocks. In addition, the clock discrepency obviously is larger when measured by the faster void clocks than by our local clocks. Wiltshire considers void clocks to be the proper basis for cosmic measurements because voids dominate the current observable universe on a relative volume basis, constituting about 76% of the total volume.

    His calculations are quite precise, subject to normal observational errors. In http://http://arxiv.org/abs/0709.2535v2" [Broken] he calculates that the accumulated discrepency of dominant void clocks compared to wall/filament clocks is 38%, as measured by void clocks.

    Wiltshire's GR math is complex. It looks logical to me, but it is beyond my mathematical ability to actually verify it. Feel free to help yourself!

    Last edited by a moderator: May 3, 2017
  11. Jan 20, 2008 #10
    Wiltshire published another http://http://arxiv.org/abs/0712.3984" [Broken] on xmas eve. It provides a slightly less technical overview of his "Fractal Bubble" theory, together with some added commentary. He also says he will be publishing two additional papers on this subject soon, which I look forward to reading.

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  12. Jan 21, 2008 #11


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    Hi Jon.

    I feel a bit uncomfortable with the terms "quasilocal (anti-) gravitational energy" in the voids. I did not notice the "anti-" in Wiltshire's papers. What do you mean by it? (Or point me to Wiltshire's definition).

  13. Jan 21, 2008 #12
    I suppose I too am a bit uncomfortable about the "anti-", because it is just my interpretation to try to make sense out of Wiltshire's technical jargon. Are you uncomfortable just because I added it, or because you think it's wrong?

    In his 12/24 paper referenced above, Wiltshire describes why some recent analysis done by others has calculated negative quasilocal energy in a k = -1 negative curvature Friedmann universe (p.10):

    "These results are expected in the current approach, since one is effectively subtracting a fiducial flat spacetime in each case, and the relative sign of energy depends on the observer. An isotropic k = 0 Friedmann observer has zero quasilocal energy in the approach of Chen, Liu, and Nestor; thus relative to the k = -1 geometry the k = 0 geometry has negative quasilocal energy, but conversely relative to the k = 0 geometry the k = -1 has positive quasilocal energy. Our viewpoint here will be that the fiducial reference point is the k = 0 geometry of the finite infinity region. This agrees with the Newtonian version of energy in the Friedmann equation, the LTB [Lemaitre-Tolman-Bondi] energy function, and with the idea that binding energy is negative."

    I interpret Wiltshire to say that, from the perspective of an observer (such as us) located in a flat (k = 0) geometry, the geometry in negatively curved (k= -1) void will have "positive" gravitational energy. Since gravitational binding energy is "negative", doesn't it make sense to interpret that positive gravitational energy is equivalent to (anti-) binding energy? I'd appreciate your analysis on this point.

    It makes sense to me that any gravitational force associated with the negative curvature in voids would be "anti-gravitational", in the sense that it adds to repulsion rather than to attraction. It also makes void clocks run relatively faster, not relatively slower. Otherwise the underdensity and negative curvature of the void would tend to cancel each other out rather than reinforce each other. At the simplest level, I can't visualize a void as being a normal gravitational well.

    Last edited: Jan 21, 2008
  14. Jan 21, 2008 #13


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    Jon, to me this is roughly analogous to the "void" between Earth and the Moon. Objects initially at rest near the Lagrangian point L1 will tend to free-fall away from it. This is not anti-gravity, but just normal gravity (and orbital dynamics), caused by the gravitational wells of the two massive orbiting bodies. Also, clocks near L1 will gain time on clocks on Earth or on the Moon. I suppose one can view the spacetime curvature at L1 to be negative, hence geodesics diverge.

    In the same way I think of void galaxies as being 'attracted' to the walls, not being 'pushed' by some anti-gravity. Maybe one should rather say that the geodesics of the void galaxies diverge due to the negative spacetime curvature there.

    Wilstshire's "quasi-local" gravitational binding energy in the voids is less negative than in the void walls, depending on what the reference point is. But I would not call that "(anti-) binding energy)"!
    Last edited: Jan 21, 2008
  15. Jan 23, 2008 #14
    Hi Jorrie,

    Hmmm, well first I think I need to change my terminology. Wiltshire's point is that the cosmic expansion is not accelerating per se; rather the acceleration is apparent only, a result of measuring the expansion rate of voids by reference to our wall clocks. If instead we referred to the dominant void clocks, Wiltshire says we would see the voids expanding at an Einstein-de Sitter rate which is appropriate for their average underdensity. This means that even in voids the expansion rate is decelerating, although it must be decelerating more slowly than in overdense regions. Deceleration of the voids must trend towards zero over time as their relative underdensity continues to increase.

    In the absence of any true accelerative force in the voids in the Wiltshire model, I guess the negative curvature by definition isn't manifested as either an attractive or a repulsive force; it's not manifested as a force at all. It is manifested only as an Einstein-de Sitter underlying Hubble expansion.

    Having said that, I don't understand Wiltshire's use of the term "positive gravitational energy". He clearly is portraying it as some kind of inverse to "negative" binding energy. Would it be more accurate to call it "kinetic energy of expansion" instead?

    I do not agree with your more general point that void galaxies are only pulled by wall galaxies and are not pushed by the intrinsic expansion of space in the void. Even if you are referring only to Wiltshire's "apparent acceleration" of the voids as measured by wall clocks [edit: or as measured by void clocks], it seems obvious to me that over time a void together with its integrated wall structure is in net expanding overall at faster than the cosmic average Hubble rate, which certainly is uncharacteristic of a gravitationally bound structure.

    I'm interpreting your push/pull argument as not being limited just to the Wiltshire model. On the assumption that's so, I'm going to write more on this subject in my thread "Hubble expansion in a contracting supercluster", which is directed more to that subject.

    Last edited: Jan 23, 2008
  16. Jan 28, 2008 #15
    2 cents

    Just to start off, I think these ideas are really interesting and deserve some real thought. I think the terminology is confusing (finite infinity regions for example) and I don't understand a lot of it, but it does attempt to open up a very sensible line of reasoning. The FLRW metric that is used in the standard model can be used to determine many things but it is a metric in which there is NO structure. Everything is distributed evenly throughout all of space. Averaging over some very large distance this appears to be true, but it is not clear that all of our observations can be interpreted with this metric.

    Consider the question "Why does the expansion of the Universe not pull our solar system apart or pull the moon and the Earth apart?" The usual answer is that gravitationally bound structures are not effected by cosmic expansion. The more correct (but in the same spirit) answer is that the solar system and our earth/moon system are not described by something like an FLRW metric. They are closer to a Schwarzschild metric if anything. Also our galaxy, our local group, and in some important ways, the filamentary structure of the Universe are not described well by an FLRW metric. He (Wiltshire) is not saying that there is some special configuration of matter that is fine tuned to produce cosmic acceleration, he is saying (I think) that if you properly take into account the observed structure of the Universe (the swiss cheese with large voids/filaments/sheets) then standard general relativity could explain our observation of acceleration.

    Sitting in the middle of a large void is like being in an FLRW metric that has a density less the rho critical and could mimic a FLRW universe at rho crit. that is accelerating. This is an interesting (and short) paper by Caldwell and Stebbins about an idea for testing this kind of hypothesis.

    Always good conversations on these forums ; )
  17. Jan 29, 2008 #16
    Hi Allday,
    I think the general view is that Hubble expansion exists as a background phenomenon everywhere in the universe, in contention against the opposing local influence of gravitational acceleration. When the local space experiences net zero, or negative expansion (gravitational collapse), then obviously gravitational acceleration is dominant in that region. The one vector is directly subtracted from the other.

    To answer your specific question, a number of calculations have been done regarding what the Hubble expansion effect is at the scale of our solar system. The answer seems to be that there is an effect, but it is utterly insignificant at our scale. One http://http://lanl.arxiv.org/abs/astro-ph/9803097v1" [Broken] says that at the scale of the Earth's orbit, it is 44 orders of magnitude smaller than the Sun's gravity. Another paper pointed out that it's far too small to explain the Pioneer anomaly, and besides that anomoly is towards us, not away from us.

    It is accurate to describe a non-expanding region of asymptotically flat vacuum around a concentrated mass as a Schwartzschild space. But that doesn't mean that anything fundamental has changed about the background Hubble expansion within that space; it just means that local gravity vector happens to be dominating the expansion vector for now. If the object has peculiar motion, then each succeeding such Schwartzchild space it departs will of course immediately rejoin the overall Hubble expansion once the gravitational influence has moved away.

    Saying that "a lack of structure causes a higher rate of expansion" is not mutually exclusive with "the existence of structure causes a lower rate of expansion." It depends on the baseline you choose to start measuring from. The baseline for mainstream cosmology is the cosmic-average Hubble rate, so that seems to leave semantic room for both "peculiar expansion" and "peculiar contraction." In the Wiltshire model, there is no "real" acceleration of expansion in voids; the "apparent" acceleration is an artifact of the differing clock rates.

    The idea that we may be located near the center of a local "Hubble Bubble" has been discussed quite a bit in the literature. Hopefully the tests described by Caldwell and Stebbins will help answer the question. Personally I tend to think it's unlikely we are in such a void -- the Hubble Bubble local redshift discrepencies are more likely due to some measurement inaccuracy or artifact, or some other effect. But who knows. In any event, the Hubble Bubble is not to be confused with the Local Void. Our Local Sheet forms part of the wall structure of the Local Void, so we are not actually inside that void. The paper you reference isn't clear about whether their measurement technique could detect indications of voids which are nearby, but which we are outside of.

    By the way, I think it's just a matter of semantics to say that if we are in the middle of a void, it violates the Copernican Principle. The Copernican Principle in no way contradicts the existence of voids and other structure, and presumably there can be an infinite number of voids and void observers, none of whom should be considered any more "privileged" than the potentially infinite number of non-void observers. In fact at present, the universe is believed to be 95% voids, by volume.

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  18. Jan 29, 2008 #17
    Hi jonmtkisco,

    Thinking of the Hubble expansion as seperate from the detailed structure of the Universe is the problem I think. What you describe is a simple way to paste together two ideas: 1. the newtonian approximation of flat, zero cosmological constant, space that contains matter in a swiss cheese structure and 2: the FLRW metric which is a solution to the Einstein Field Equations for a given set of omegas( matter, lambda, radiation ...) in a perfectly smooth universe.

    The solution of the Friedman equation gives you the evolution of the scale factor (and therefore the Hubble parameter) with time in the smooth FLRW Universe.

    H(t) = \frac{ \dot{a(t)} }{a(t)}

    The pasting of this expansion onto the lumpy universe is what I think is the important issure here. Our local Hubble parameter could be derived using standard general relativity, but with metrics that more accurately describe our observed universe. If not a completely new metric than at least a pasting together of different FLRW metrics that match the swiss cheese nature of the observations better.

    Just to be a little more clear, Im not saying that this is without a doubt the solution to the dark energy problem, I just think that more people should take into account the bumpy nature of the current Universe when interpreting observations and try to crank out some GR with no dark energy and something other than the FLRW metric. By the way, do you have any links to research that shows that we are in a sheet, filament, or void? I was not aware that we had placed ourselves within one of these structures with any survey data.

    I really will have to read the paper before I post again ; )

    Also, I aggree that it is not a violation of the Copernican Principle to be located at a void center (just as it wouldn't be a violation if we happened to be in the CMB rest frame)
    Last edited: Jan 29, 2008
  19. Jan 29, 2008 #18
    Hi Allday,
    I agree, but I'd say it the other way around: A lumpy matter structure has been overlaid onto a smooth, constant primordial FLRW Hubble expansion. The gravitational lumpiness both distorts the expansion rate locally, and causes the overall expansion to permanently lose expansion "momentum". (If there is dark energy, then it is believed to be reaccelerating that momentum.)

    As mentioned in my thread "Hubble expansion within a collapsing supercluster", Chernin et al are developing a lumpy version of FLRW based on swiss cheese "vacuoles". They have not yet suggested that it provides an alternative to dark energy, in fact their modelling all assumes dark energy.

    Recent observations indicate that our Local Sheet is part of the wall structure of our Local Void. Please see the Tully papers referenced in my "Hubble expansion..." thread mentioned above. The matter is not entirely certain, because a big chunk of the void is blocked from our view by the "Zone of Avoidance", the body of our Milky Way galaxy.

    Last edited: Jan 29, 2008
  20. Jan 29, 2008 #19
    After having read the paper

    Thanks for all the references jon, Ill take a look.

    So, I read the short one (http://arxiv.org/abs/0709.0732) "Exact solution to the averaging problem in cosmology" I am a lot clearer now than I was before on what Wiltshire is doing. I wrongly assumed he was doing something like calculating the consequences of us being in a void or Hubble Bubble, but now I see he is (in rough language) averaging a solution of the Einstein equations in voids (where we are not) and void walls (where we are). This gives rise to "bare" and "dressed" values of the cosmological parameters. The dressed values are those measured by us as wall observers and can imitate those that would be expected in FLRW model with dark energy.

    Really cool stuff. What would be the observations that could discriminate dark energy from an averaging solution?
  21. Jan 29, 2008 #20


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    Wiltshire has made some specific predictions, though by his own admission they are very hard to measure. I can't remember the exact details but from memory I think it relates to the average dispersion (or peculiar) velocity of galaxies. In other words, on average, what is the average deviation of galaxies from a perfectly linear Hubble law. I think this is in his papers somewhere, I just remember him talking about this at a conference recently.

    Really though, this is a theoretical not an observational problem. The debate boils down to whether or not spatial averaging a lumpy universe gives you the correct background expansion. This is a question that must be solve theoretically. Actually the problem is that 95% of the cosmology community believe this is solved already and don't bother even refuting the papers of Wiltshire and others, since they are regarded as simply being flawed reasoning.

    To say there is a debate about averaging in cosmology would be misleading. What is happening is that a minority are making very loud noises about it and the majority have already considered these ideas, come to the conclusion that they are wrong and aren't really paying much attention. I'm not taking sides either way but I think that is an accurate (if blunt) depiction of things at present. Note that the work of Chernin and co-workers has nothing at all to do with this issue.

    If I may digress for a moment, this points to a bit of an issue with the way research works. There is little value in a researcher spending time refuting these kind of ideas, since the majority of the community aren't interested and so don't need convincing and the minority are the minority, which means a much smaller group of people who might cite your work (and in research citations make the world go around). I know of only one paper that systematically argues against dark energy being due to averaging not working in GR and I wouldn't hold your breath for more.

    The problem with this is that no one has actually made a systematic calculation that demonstrates that the effect of perturbations is large enough to spoof the data to look like dark energy. If you read Wiltshire's papers very closely, he spends a lot of time talking about 'finite infinity', 'quasi-local energy' and other phrases that he introduces, which he argues justifies the form of the improved FRW equations that he writes down. But again, if you read carefully you will see that these equations contain completely free parameters whose values are determined by fitting to data. This is not a robust argument, nor is it even a proof in principle. He is arguing against very reasonable approximations (read any standard textbook for detailed discussion) without actually doing any calculation to demonstrate that the effect is any where near big enough.

    Wiltshire criticizes Rocky Kolb and his group (who have been working on lumpy models for a long time) yet they at least are trying to do the theoretical calculation, even if they aren't getting anywhere with it very fast.

    No one disputes that averaging introduces some error, but the standard textbook calculation puts the error at around [tex]10^{-4}[/tex] or something like that from memory. In other words the difference in expansion rate you would expect due to average than in the real world is less than 0.01%. The same applies to any difference in the luminosity distance, clock rates or any other quantity. The challenge for anyone wanting to claim what Wiltshire and others do is why the error is in fact 5 orders of magnitude bigger than expected. That's a pretty tough call, not impossible certainly, but a convincing calculation has yet to be demonstrated.
    Last edited: Jan 29, 2008
  22. Jan 30, 2008 #21
    Hi Wallace,

    I agree that there are plenty of cosmologists who are skeptical that the "backreaction" from cosmological inhomogeneity could be large enough to replace dark energy. They may be right, but hopefully this will get resolved soon. I haven't seen too many who have commented specifically on Wiltshire's point that negative curvature in voids reinforces the effect of inhomogeneity and therefore may push it up to the necessary magnitude.

    In any event, the subject does seem to be getting a fair amount of discussion and debate recently. Here's a sampling of recent papers on the subject -- (this list is not all inclusive.) Some cite Wiltshire, others don't.

    "[URL [Broken] [astro-ph] 16 Jan 2008"]Paranjape & Singh, 1/08 [/URL]
    "[URL [Broken] [astro-ph] 22 Jan 2008"]Nan Li, Seikel, Schwarz 1/08[/URL]
    "[URL [Broken] [astro-ph] 17 Jan 2008"]Rasanen 1/08[/URL]
    "[URL [Broken] [math-ph] 3 Jan 2008"]Carfora & Buchert 1/08[/URL]
    "[URL [Broken] [astro-ph] 18 Dec 2007"]Beherend, Brown, Robbers 12/07[/URL]
    "[URL [Broken] [gr-qc] 3 Dec 2007"]Buchert 12/07[/URL]
    "[URL [Broken] [astro-ph] 10 Sep 2007"]Mattsson & Ronkainen 9/07[/URL]
    "[URL [Broken] [astro-ph] 19 Jun 2007"]Vanderveld et al 6/07[/URL]
    "[URL [Broken] [gr-qc] 13 Apr 2007"]Coley4/07[/URL]

    Happy reading!

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  23. Jan 30, 2008 #22


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    Sure there is discussion, but it is amongst the small minority who think there is something in this idea at all. Most have decided that the standard approximation is robust and there is no good reason that it would break down so severely and unexpectedly. This is why this will not be resolved soon, since only the small minority who write those papers don't believe it has been resolved already. I'm pressed for time at the moment, but could you indicate which if any of the papers you list argue against the whole concept?

    As I mentioned previously, I know of only a single referred paper that has done this so I'd be curious to read any others.
  24. Jan 31, 2008 #23


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    I agree with your perspective. the idea of explaining acceleration by inhomogeneity has been around since before 2005 and for the great majority it's goose was cooked by the Ishibashi and Wald paper published 2006. Robert Wald is a major figure for sure.

    Compared with the main body of work on dark energy and the cosmological constant, there has only been a trickle of papers of this type, and I don't think Wiltshire is even the most prolific or cited in that small minority. I would put Biswas ahead of him and maybe Buchert.

    I am not saying right or wrong, just that the general consensus noticed the idea around 2005 and dismissed it around 2006 and now it is kind of fringe (whatever merits)

    Can the Acceleration of Our Universe Be Explained by the Effects of Inhomogeneities?
    Akihiro Ishibashi, Robert M. Wald
    20 pages, 1 figure, published Class.Quant.Grav. 23 (2006) 235-250
    (Submitted on 27 Sep 2005)

    "No. It is simply not plausible that cosmic acceleration could arise within the context of general relativity from a back-reaction effect of inhomogeneities in our universe, without the presence of a cosmological constant or 'dark energy'. We point out that our universe appears to be described very accurately on all scales by a Newtonianly perturbed FLRW metric. (This assertion is entirely consistent with the fact that we commonly encounter [tex]\delta \rho/\rho > 10^{30}[/tex].) If the universe is accurately described by a Newtonianly perturbed FLRW metric, then the back-reaction of inhomogeneities on the dynamics of the universe is negligible. If not, then it is the burden of an alternative model to account for the observed properties of our universe. We emphasize with concrete examples that it is not adequate to attempt to justify a model by merely showing that some spatially averaged quantities behave the same way as in FLRW models with acceleration. A quantity representing the 'scale factor' may 'accelerate' without there being any physically observable consequences of this acceleration. It also is not adequate to calculate the second-order stress energy tensor and show that it has a form similar to that of a cosmological constant of the appropriate magnitude. The second-order stress energy tensor is gauge dependent, and if it were large, contributions of higher perturbative order could not be neglected. We attempt to clear up the apparent confusion between the second-order stress energy tensor arising in perturbation theory and the 'effective stress energy tensor' arising in the 'shortwave approximation.' "

    It will be interesting to see if anything happens. But I think it may have been downhill since 2006. Here is an invited review paper by Copeland Sami and Tsujikawa
    Dynamics of dark energy
    Edmund J. Copeland, M. Sami, Shinji Tsujikawa
    93 pages, 26 figures, Invited Review published in the International Journal of Modern Physics D15 (2006) 1753-1936
    (Submitted on 8 Mar 2006)

    "In this paper we review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating Universe... "

    In this 94 page review with over 500 citations, the idea of explaining acceleration this way is mentioned briefly in two paragraphs, mostly devoted to paraphrasing the argument by Wald and Ishibashi, which is their reference [510]. Wiltshire is not mentioned by name but a paper of his is one of a dozen or so papers of the same type which are lumped together as reference [511].
    Last edited: Jan 31, 2008
  25. Jan 31, 2008 #24


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    Yes Ishibashi and Wald, that was the 'one' paper I was thinking of, I couldn't remember who wrote it. Thanks Marcus, always good for a reference :)

    To be honest I must admit I wasn't completely taken with their arguments, I found they mainly rehash the kind of textbook justifications for averaging rather than a more rigorous calculation demonstrating the the approximation really is fine. This criticism is a bit harsh since that calculation is incredibly difficult, which is why it is not done.
  26. Jan 31, 2008 #25


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    Hi Wallace! I think Wald and Ishibashi probably overstate. The review article by Copeland et al take a more balanced view and are more mellow. they repeat Wald arguments and they say well there is not much if any indication that Wiltshire's idea is right, but wouldn't it be nice if it WERE :-) and then we could explain everything without any novel dark energy.

    So it is a minor or fringe idea but it is still alive and getting some attention from a few people. That said we can look at the small bunch of papers about this and see who the main proponents are. Within that group I am impressed by how much Biswas is cited. Here is a list that gives LINKS TO ABSTRACTS so anyone who is curious can quickly see what the papers are about:
    this is Spires with the command FIND C GR-QC/0503099
    http://www.slac.stanford.edu/spires/find/hep?c=GR-QC/0503099 [Broken]

    If I copy and past this, it will not have the links but if you just go to that Spires URL then you get the links and information about how much the various papers have been cited.

    this is not a very selective list. It is just the 20 papers which cited Wiltshire's main 2005 paper about it. That Wiltshire paper got 20 cites, and some of the subsequent ones by other people (who cited Wiltshire) have in turn gotten more than 20.

    1) Local Void vs Dark Energy: Confrontation with WMAP and Type Ia Supernovae.
    Stephon Alexander, Tirthabir Biswas (Penn State U.) , Alessio Notari (McGill U. & CERN) , Deepak Vaid (Penn State U.) . IGPG-07-2-1, Dec 2007. 26pp.
    e-Print: arXiv:0712.0370 [astro-ph]
    Cited 5 times

    2) The Spatial averaging limit of covariant macroscopic gravity: Scalar corrections to the cosmological equations.
    Aseem Paranjape, T.P. Singh (Tata Inst.) . Mar 2007. 24pp.
    Published in Phys.Rev.D76:044006,2007.
    e-Print: gr-qc/0703106
    Cited 14 times

    3) Swiss-Cheese Inhomogeneous Cosmology and the Dark Energy Problem.
    Tirthabir Biswas (McGill U. & Penn State U.) , Alessio Notari (McGill U.) . IGPG-07-2-2, Feb 2007. 35pp.
    e-Print: astro-ph/0702555
    Cited 10 times

    4) Cosmic clocks, cosmic variance and cosmic averages.
    David L. Wiltshire (Canterbury U.) . Feb 2007. 72pp.
    Published in New J.Phys.9:377,2007.
    e-Print: gr-qc/0702082
    Cited 18 times

    5) Nonlinear Structure Formation and Apparent Acceleration: An Investigation.
    Tirthabir Biswas (McGill U.) , Reza Mansouri (McGill U. & Sharif U. of Tech.) , Alessio Notari (McGill U.) . Jun 2006. 57pp.
    Published in JCAP 0712:017,2007.
    e-Print: astro-ph/0606703
    Cited 32 times

    6) Correspondence between kinematical backreaction and scalar field cosmologies: The `Morphon field'.
    Thomas Buchert (Bielefeld U. & Munich U.) , Julien Larena, Jean-Michel Alimi (LUTH, Meudon) . Jun 2006. 36pp.
    Published in Class.Quant.Grav.23:6379-6408,2006.
    e-Print: gr-qc/0606020
    Cited 25 times

    7) Dark matter, and its darkness.
    Dharam Vir Ahluwalia . ASGBG-PREPRINT:-20-03-2006AH, Mar 2006. 12pp.
    * Brief entry *.
    Published in Int.J.Mod.Phys.D15:2267-2278,2006.
    e-Print: astro-ph/0603545
    Cited 1 time

    8) Dynamics of dark energy.
    Edmund J. Copeland (Nottingham U.) , M. Sami (Jamia Millia Islamia) , Shinji Tsujikawa (Gunma Coll. Tech.) . Mar 2006. 84pp.
    Published in Int.J.Mod.Phys.D15:1753-1936,2006.
    e-Print: hep-th/0603057
    Cited 434 times

    9) Structured frw universe leads to acceleration: a non-perturbative approach.
    Reza Mansouri (McGill U.) . Dec 2005.
    e-Print: astro-ph/0512605
    Cited 28 times

    10) An inhomogeneous alternative to dark energy?
    Havard Alnes (Oslo U.) , Morad Amarzguioui (Inst. Theor. Astrophys., Oslo) , Oyvind Gron (Oslo Coll. & Oslo U.) . Dec 2005. 8pp.
    Published in Phys.Rev.D73:083519,2006.
    e-Print: astro-ph/0512006
    Cited 45 times

    11) Asymmetric inflation: Exact solutions.
    Roman V. Buniy (Oregon U.) , Arjun Berera (Edinburgh U.) , Thomas W. Kephart (Vanderbilt U.) . Nov 2005. 42pp.
    Published in Phys.Rev.D73:063529,2006.
    e-Print: hep-th/0511115
    Cited 13 times

    12) Long-wavelength modes of cosmological scalar fields.
    Marcin Jankiewicz, Thomas W. Kephart (Vanderbilt U.) . Oct 2005. 12pp.
    Published in Phys.Rev.D73:123514,2006.
    e-Print: hep-ph/0510009
    Cited 6 times

    13) On globally static and stationary cosmologies with or without a cosmological constant and the dark energy problem.
    Thomas Buchert (Munich U.) . Sep 2005. 33pp.
    Published in Class.Quant.Grav.23:817-844,2006.
    e-Print: gr-qc/0509124
    Cited 28 times

    14) Can a dust dominated Universe have accelerated expansion?
    Havard Alnes (Oslo U.) , Morad Amarzguioui (Inst. Theor. Astrophys., Oslo) , Oyvind Gron (Oslo Coll. & Oslo U.) . Jun 2005. 11pp.
    Published in JCAP 0701:007,2007.
    e-Print: astro-ph/0506449
    Cited 21 times

    15) Inflessence: A Phenomenological model for inflationary quintessence.
    Vincenzo F. Cardone, A. Troisi (Salerno U. & INFN, Salerno) , S. Capozziello (Naples U. & INFN, Naples) . Jun 2005. 12pp.
    Published in Phys.Rev.D72:043501,2005.
    e-Print: astro-ph/0506371
    Cited 14 times

    16) Late-time inhomogeneity and acceleration without dark energy.
    John W. Moffat (Perimeter Inst. Theor. Phys. & Waterloo U.) . May 2005. 10pp.
    Published in JCAP 0605:001,2006.
    e-Print: astro-ph/0505326
    Cited 30 times

    17) The Effects of gravitational back-reaction on cosmological perturbations.
    Patrick Martineau (McGill U.) , Robert H. Brandenberger (McGill U. & Brown U.) . May 2005. 9pp.
    Published in Phys.Rev.D72:023507,2005.
    e-Print: astro-ph/0505236
    Cited 17 times

    18) Type Ia supernovae tests of fractal bubble universe with no cosmic acceleration.
    Benedict M.N. Carter, Ben M. Leith (Canterbury U.) , S.C.Cindy Ng (Singapore Natl. U.) , Alex B. Nielsen, David L. Wiltshire (Canterbury U.) . Apr 2005. 10pp.
    e-Print: astro-ph/0504192
    Cited 10 times

    19) Large scale cosmological inhomogeneities, inflation and acceleration without dark matter.
    John W. Moffat (Perimeter Inst. Theor. Phys. & Waterloo U.) . Apr 2005. 10pp.Cited 9 times
    e-Print: astro-ph/0504004

    20) Cosmic microwave background, accelerating Universe and inhomogeneous cosmology.
    John W. Moffat (Perimeter Inst. Theor. Phys. & Waterloo U.) . Feb 2005. 18pp.
    Published in JCAP 0510:012,2005. Cited 37 times
    e-Print: astro-ph/0502110
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