Can Higher Order Curvature Theories of Gravity Solve the Dark Matter Puzzle?

[Chronos]

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

 

[turbo]

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.

 

[Garth]

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.//...// That's a pretty big number, and it's giving some folks fits.

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

 

[turbo]

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

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.

 

[nightcleaner]

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 anyone 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

 

[turbo]

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.

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.

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 anyone 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

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.

 

[GENIERE]

...This is done by putting parallel conducting plates VERY close to one another...

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.

 

[Chronos]

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

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.

 

[Chronos]

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

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 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.

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.

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.

Huh? Symbolic logic suggests that assertion may be flawed.

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.

See above. If the ground state energy itself cannot be sensed, how might you go about sensing and measuring fluctuations relative to it?

 

[turbo]

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

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.

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.

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.

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?

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.

 

[Garth]

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

 

[nightcleaner]

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.
QUOTE]

Hi turbo-1
I have been thinking about the 120 oom problem, but I need to look at it some more. At first blush, 120 oom does seem like a large number, but it may not be out of bounds when comparing our current environment to that found on the Planck scale. In Planck time (the time it would take light to travel a Planck length of 10E-33 cm) the universe (if my memory and calculator don't fail me) at 13.7 Billion years is about 4.32 E 59 Planck times from the origin. In four dimensions, this would be the universal Planck radius, so 8.64 Planck times across. Then the area of a slice through the universe would be 1.7 x 10 E 120 Planck Times squared. I did this calculaton on scrap paper at work last night and havnt checked it in detail, but that seems about right, and it is close to the 120 oom you mention. Also, the unit would be time squared, which is matches the inverse square law and is appropriate to discussions of energy. Does this seem to have any bearing on the ZPE problem?

Further, I roughly calculate that the universe in 3 D volume is about 8 x 10 E 178 Planck spheres. I have seen a formula for calculating volume equivalents in 4 D but don't trust my memory for that. I'll have to try to find it again, since it now seems to be of interest.

My point is that given the age of the universe, and comparing the inverse square of one Planck unit to the calculated area of a plane through the universe, gives very nearly the 120 oom. Maybe it isn't such an outlandish number after all?

nc

This

 

[turbo]

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

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.

 

[ohwilleke]

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

 

[ohwilleke]

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.

 

[marcus]

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.

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 possesses 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.

 

[Garth]

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

 

[ohwilleke]

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

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 article you cite is about physical evidence for DE.

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.

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 possesses 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."

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.

can't 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.

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.

 

[turbo]

Cadoni has made another effort here: http://arxiv.org/abs/gr-qc/0312054 but it violates the equivalence principle.

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.)

Apart from the breakdown of the equivalence principle, a gravitational theory described by the action (1) in which the parameter  is a function of the mass M of the source poses also huge interpretation problems. Implicitly we are assuming the existence of a “cosmic” scalar field ' whose self-coupling the potential V ) and its coupling with the matter (the coupling function F) are determined by the distributions of the sources for the gravitational field. We do not have a definite prescription of how the information about the distribution of matter has to be encoded on the form of the functions F and V . There is no general argument, no principle, behind our Eq. (17). Its only justification is the accordance with the observed rotation curves of the galaxies. For this reason our model, at least in the present context, cannot have a fundamental but just a phenomenological character. Independently of the fundamental, still unknown physics that could lie behind our phenomenological model, it is likely that the information about the distribution of matter has to be encoded in the cosmic field, trough the form of the functions V (', M) and F(', M), in a non local way. We are leaving the Einsteinian paradigm and moving toward a Machian description of the gravitational interaction.

 

[ohwilleke]

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.

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

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

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.

 

[ohwilleke]

Its only justification is the accordance with the observed rotation curves of the galaxies. For this reason our model, at least in the present context, cannot have a fundamental but just a phenomenological character. Independently of the fundamental, still unknown physics that could lie behind our phenomenological model, it is likely that the information about the distribution of matter has to be encoded in the cosmic field, trough the form of the functions V (', M) and F(', M), in a non local way.

It isn't clear to me that you actually need to break equivalence to achieve fits to galactic rotation curves, indeed, that it what is so attractive about Bekenstein's formulation. And, if the only reason you are breaking equivalence is to do that, Occam starts to rear his ugly head.

 

[ohwilleke]

One more point about the originally posted article. Look at the Milky Way fit they propose. It is not nearly as good of a fit as the ones that the MOND guys are producing en masse here: http://www.astro.umd.edu/~ssm/mond/mdlg.gif and here: http://www.astro.umd.edu/~ssm/mond/mdlg.gif_2 for example. See page 7 of this: http://www.arxiv.org/PS_cache/astro-ph/pdf/0411/0411114.pdf where they have basically a straight line running through a data set the seems to show some definite curves.

 

[turbo]

It isn't clear to me that you actually need to break equivalence to achieve fits to galactic rotation curves, indeed, that it what is so attractive about Bekenstein's formulation. And, if the only reason you are breaking equivalence is to do that, Occam starts to rear his ugly head.

My model of gravitation needs to break equivalence, which is why I am heartened by Cadoni's paper. He says that his model must describe an underlying phenomonology, and I believe that my model of gravitation can supply the behavior that he is modeling. In my model, the virtual particle/antiparticle pairs of the zero point energy fields have equivalent inertial masses, but their gravitational masses differ due to a higher infall rate for antiparticles. This provides the mechanism for polarization and "self-coupling".

 

[Chronos]

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

It is measurable. Here are some less technical discussions:

http://www.astro.ucla.edu/~wright/cosmo_constant.html
Vacuum Energy Density, or How Can Nothing Weigh Something?
[Here is the paper by Cardona and Tejeiro referenced by Ned Wright in link above]
http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v493n1/36511/36511.html
Can Interplanetary Measures Bound the Cosmological Constant?

http://www.arxiv.org/abshep-ph/0405089
Problems of vacuum energy and dark energy

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000063000007000620000001&idtype=cvips&gifs=yes
Vacuum catastrophe: An elementary exposition of the cosmological constant problem

http://www.arxiv.org/abs/quant-ph/0105053
Quantum vacuum fluctuations

And for some more technical material:

http://www.arxiv.org/abs/astro-ph/0105396
Constraints on Omega_m, Omega_L, and Sigma_8, from Galaxy Cluster Redshift Distributions

http://www.arxiv.org/abs/astro-ph/0305051
Cosmological results from the 2dF Galaxy Redshift Survey

http://www.arxiv.org/abs/astro-ph/0303388
Constraining the dark energy with galaxy clusters X-ray data

 

[turbo]

It is measurable. Here are some less technical discussions:

http://www.astro.ucla.edu/~wright/cosmo_constant.html
Vacuum Energy Density, or How Can Nothing Weigh Something?
[Here is the paper by Cardona and Tejeiro referenced by Ned Wright in link above]
http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v493n1/36511/36511.html
Can Interplanetary Measures Bound the Cosmological Constant?

http://www.arxiv.org/abshep-ph/0405089
Problems of vacuum energy and dark energy

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000063000007000620000001&idtype=cvips&gifs=yes
Vacuum catastrophe: An elementary exposition of the cosmological constant problem

http://www.arxiv.org/abs/quant-ph/0105053
Quantum vacuum fluctuations

And for some more technical material:

http://www.arxiv.org/abs/astro-ph/0105396
Constraints on Omega_m, Omega_L, and Sigma_8, from Galaxy Cluster Redshift Distributions

http://www.arxiv.org/abs/astro-ph/0305051
Cosmological results from the 2dF Galaxy Redshift Survey

http://www.arxiv.org/abs/astro-ph/0303388
Constraining the dark energy with galaxy clusters X-ray data

"Measurable" is just a bit strong (like the Pope is a bit Catholic). Trying to mathematically establish constraints on the absolute energy density of the ZPE fields is a far cry from measuring that energy, and there is not a single paper here that claims to have accomplished this in even a rudimentary manner. You may want to visit the first link you cited (Ned Wright) and pursue his thought that some suppression effect may reduce the net energy density of the quantum vacuum to zero. That "suppression effect" may be related to the fact that the ZPE field is the ground state of our universe, and is indistinguishable from a vacuum at zero degrees absolute.

 

[Chronos]

"Measurable" is just a bit strong (like the Pope is a bit Catholic). Trying to mathematically establish constraints on the absolute energy density of the ZPE fields is a far cry from measuring that energy, and there is not a single paper here that claims to have accomplished this in even a rudimentary manner. You may want to visit the first link you cited (Ned Wright) and pursue his thought that some suppression effect may reduce the net energy density of the quantum vacuum to zero. That "suppression effect" may be related to the fact that the ZPE field is the ground state of our universe, and is indistinguishable from a vacuum at zero degrees absolute.

Really? Not a single paper cited claims the vacuum energy density has been measured? A few examples suggesting otherwise:

from the paper Vacuum catastrophe: An elementary exposition of the cosmological constant problem
"Quantum field theory predicts a very large energy density for the vacuum, and this density should have large gravitational effects. However these effects are not observed, and the discrepancy between theory and observation is an incredible 120 orders of magnitude."

from the paper Quantum vacuum fluctuations
"The existence of irreducible field fluctuations in vacuum is an important prediction of quantum theory. These fluctuations have many observable consequences... But the vacuum energy density calculated by adding field mode energies is much larger than the density observed around us through gravitational phenomena."

from the paper Problems of vacuum energy and dark energy http://www.arxiv.org/abs/hep-ph/0405089
"The mechanisms which may lead to cancellation of almost infinite vacuum energy down to the astronomically observed value are discussed."

 

[turbo]

Really? Not a single paper cited claims the vacuum energy density has been measured? A few examples suggesting otherwise:

from the paper Vacuum catastrophe: An elementary exposition of the cosmological constant problem
"Quantum field theory predicts a very large energy density for the vacuum, and this density should have large gravitational effects. However these effects are not observed, and the discrepancy between theory and observation is an incredible 120 orders of magnitude."

from the paper Quantum vacuum fluctuations
"The existence of irreducible field fluctuations in vacuum is an important prediction of quantum theory. These fluctuations have many observable consequences... But the vacuum energy density calculated by adding field mode energies is much larger than the density observed around us through gravitational phenomena."

from the paper Problems of vacuum energy and dark energy http://www.arxiv.org/abs/hep-ph/0405089
"The mechanisms which may lead to cancellation of almost infinite vacuum energy down to the astronomically observed value are discussed."

Dear Chronos:

Measuring the asolute energy of the quantum vacuum has never been accomplished, and it probabably never will. Please note that there is a huge difference between estimating the energy of the vacuum and measuring the energy of the vacuum.

 

[turbo]

To reiterate a the 120 OOM energy deficit of the quantum vacuum in real-world terms:

1) Feinman has been quoted as saying that there is enough vacuum energy in a volume the size of a light bulb to evaporate all the oceans on Earth.

2) It has been calculated that if the mass equivalence of the energy of the quantum vacuum were expressed, the universe would collapse to a volume not too much larger than the Earth.

It is difficult to even conceive of energies of this magnitude, but we must come to terms with the fact that such energies are entirely suppressed (or very nearly so) in our universe. BTW, Andrei Sakharov is on record as having recommended a ban on experimentation regarding ZPE field energies due to the potentially "catastrophic" effects if such energies were to be released.

 

[ohwilleke]

Really? Not a single paper cited claims the vacuum energy density has been measured? A few examples suggesting otherwise:

from the paper Vacuum catastrophe: An elementary exposition of the cosmological constant problem
"Quantum field theory predicts a very large energy density for the vacuum, and this density should have large gravitational effects. However these effects are not observed, and the discrepancy between theory and observation is an incredible 120 orders of magnitude."

from the paper Quantum vacuum fluctuations
"The existence of irreducible field fluctuations in vacuum is an important prediction of quantum theory. These fluctuations have many observable consequences... But the vacuum energy density calculated by adding field mode energies is much larger than the density observed around us through gravitational phenomena."

from the paper Problems of vacuum energy and dark energy http://www.arxiv.org/abs/hep-ph/0405089
"The mechanisms which may lead to cancellation of almost infinite vacuum energy down to the astronomically observed value are discussed."

I have to agree that none of the three quotes above state that energy density has been measured. Inded, all three appear to state that vacuum energy has been predicted but not observed, casting considerable doubt on the theories which form the basis of the predictions.

 

[marcus]

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

Thanks for the link Garth. Also thanks to both you and Willeke for comment.
As I said in my post, I am myself not prepared to make sense out of these things or discuss them intelligently. I am glad to see you both trying.

It does seem as if (I think Willeke is making this point) you dispense with Dark Matter---by explaining galaxy rotation curves some other way----then it seems like you need more Dark Energy simply to make Omega = 1.

And putting in more Dark Energy (simply to achieve the observed spatial flatness) is going to cause other problems.

I guess I need to go back and read Willeke post (#18) more, to see if that makes it clearer.

 

[marcus]

this is from Willeke post #18

... 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,...

this is an interesting idea. i wish you or somebody would write up something along these lines, with some sample values of things calculated

as you said afterwards, your main point is that a lot of current cosmology is based on assuming CDM, so if you pull out that key assumption it opens up a lot of different possible ways to reconfigure and re-balance the books

cold dark matter is the lid on a can of worms, apparently

I find the prospect of theoretical disorder maybe a little intimidating and yet...I tend to sympathize with what you say about the actual candidates for DM seeming, at least to anyone but a particle physicist, yucky.

 

[turbo]

Getting rid of CDM is only the tip of the iceberg. If you manage to eliminate CDM and try to keep all the rest of the standard model intact, a huge mess will ensue. The "fudge factors" propping up the standard model are inextricably intertwined. The trick is to come up with a model for gravitation that not only eliminates the necessity for CDM, but cleans up other outstanding problems at the same time.

My model of polarized ZPE fields gets rid of DM, DE, curved GR space-time, and proposed gravity-mediating entities like the graviton and the Higgs boson. It explains inertia and gravitation as interaction between masses and the local vacuum fields, eliminating action at a distance and endowing GR with a semi-Machian quality by which gravitation and inertia can be explained without invoking GR space-time curvature. This model preserves the wave model of EM propogation and explains gravitational lensing and cluster lensing in terms of classical optics. It also explains how galactic clusters can remain gravitationally bound with seemingly insufficient matter. I have not finished adding references to the paper, but I do have a preliminary non-technical summary completed.

If anybody here would like a copy of the paper (MS Word format w/ 2 illustrations), just drop me a message. You can bash away at it all you'd like, as long as you will tell me why you believe it to be in error. It is a work in progress, but it is logically consistent and elegant and it is falsifiable by at least three practical experiments - perhaps you can suggest more.

 

[Chronos]

I have to agree that none of the three quotes above state that energy density has been measured. Inded, all three appear to state that vacuum energy has been predicted but not observed, casting considerable doubt on the theories which form the basis of the predictions.

Actually, what they are saying is what has been observed [measured] does not agree with predicted values. Try this by John Baez:
http://math.ucr.edu/home/baez/vacuum.html
We can measure the energy density of the vacuum through astronomical observations that determine the curvature of spacetime. All the measurements that have been done agree that the energy density is VERY CLOSE TO ZERO. In terms of mass density, its absolute value is less than 10-26 kilograms per meter. In terms of energy density, this is about 10-9 joules per cubic meter.

 

[turbo]

Actually, what they are saying is what has been observed [measured] does not agree with predicted values. Try this by John Baez:
http://math.ucr.edu/home/baez/vacuum.html
We can measure the energy density of the vacuum through astronomical observations that determine the curvature of spacetime. All the measurements that have been done agree that the energy density is VERY CLOSE TO ZERO. In terms of mass density, its absolute value is less than 10-26 kilograms per meter. In terms of energy density, this is about 10-9 joules per cubic meter.

On the page you cited, John Baez gave you almost the same answers for the 120 OOM disconnect that I gave you above. The huge energy disparity arises from the ways that quantum theory and GR treat energies. In QT, the ZPE energy is generally expressed in relation to a theoretical empty reference frame that cannot exist in our universe. In GR energy differences can be measured, but "absolute" energies cannot. In GR, all energies must be measured relative to some standard. We must be prepared to accept that if the ZPE is the ground state of our universe, we cannot measure its "absolute" energy without access to a theoretical pure vacuum outside our universe.

Interestingly, John Baez had this to say at the bottom of that page:

John Baez[/URL]]The moral is: for a question like this, you need to know not just the answer but also the assumptions and reasoning that went into the answer. Otherwise you can't make sense of why different people give different answers.

Amen! Epistemology is a much-misunderstood enterprise, and it is often reviled and attacked by those who are most attached to the "status quo" and/or are the least intellectually-equipped to appreciate its value in the advancement of science. It is essential however, if we are to see through the biases and preconceptions that blind us to a deeper understanding of our universe.

"How does it happen that a properly endowed natural scientist comes to concern himself with epistemology? Is there no more valuable work in his specialty? I hear many of my colleagues saying, and I sense it from many more, that they feel this way. I cannot share this sentiment. ...Concepts that have proven useful in ordering things easily achieve such an authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they come to be stamped as 'necessities of thought,' 'a priori givens,' etc. The path of scientific advance is often made impassable for a long time through such errors. For that reason, it is by no means an idle game if we become practiced in analyzing the long common place concepts and exhibiting those circumstances upon which their justification and usefulness depend, how they have grown up, individually, out of the givens of experience. By this means, their all-too-great authority will be broken."

Einstein

 

[Chronos]

On the page you cited, John Baez gave you almost the same answers for the 120 OOM disconnect that I gave you above. The huge energy disparity arises from the ways that quantum theory and GR treat energies. In QT, the ZPE energy is generally expressed in relation to a theoretical empty reference frame that cannot exist in our universe. In GR energy differences can be measured, but "absolute" energies cannot. In GR, all energies must be measured relative to some standard.

I think you have it backwards. To quote John Baez: "... quantum field theory and general relativity have really different attitudes towards the energy density of the vacuum. The reason is that quantum field theory only cares about energy differences. If you can only measure energy differences, you can't determine the energy density of the vacuum."

With respect to GR, Baez says this: "As far as we know, you can only determine the energy density of the vacuum by experiments that involve general relativity - namely, by measuring the curvature of spacetime."

Baez further states this, as indicated in my last post:
"We can measure the energy density of the vacuum through astronomical observations that determine the curvature of spacetime. All the measurements that have been done agree that the energy density is VERY CLOSE TO ZERO. In terms of mass density, its absolute value is less than 10-26 kilograms per meter. In terms of energy density, this is about 10-9 joules per cubic meter."