# Mod Gravity Theory/Dark Matter?

1. Oct 29, 2007

### MonstersFromTheId

Dark matter seems to have the upper hand at the moment, at least with what I read.

But now I keep hearing about Modified Gravity Theory as a alternative explanation for the large structure of the Universe, (often paired with comparisons between Dark Matter, and what was once called the "luminiferous ether").

How much support has MGT garnered at this point? Is this a serious point of view, or something that belongs more in the "debunking" section of the forum?

What has been "modified" with respect to gravitational theory?

2. Oct 29, 2007

### Wallace

There are a number of modified gravity schemes that have been proposed. Early suggestions altered Newtonian gravity (known as Modified Newtonian Dynamics or MOND) and more recently this has been extended to General Relativity in a theory known as Tensor Vector Scalar gravity (TVS). By analogy with GR going to Newtonian in the low mass limit, TVS reduces to MOND.

The basics of MOND are not so much a change in gravity as such but a change in the way gravity accelerates mass. Instead of the usual Newtons Second Laws, F=ma, MOND suggests that we have F=m µ(a/a0) a. The function µ(x) describes the modification and depends on a new parameter a0 that is suggested to be a fundamental constant. There are various forms of µ(x) that have been proposed. Try having a look at the Wikipedia article on MOND for some more info.

There are also a large number of modified gravity theories that attempt to deal with dark energy, i.e. they explain the observations that lead us to think dark energy exists as a modified gravity in a similar fashion to how MOND is supposed to do away with the need for dark matter.

As far as I'm aware no one has proposed a modified gravity theory that consistently accounts for all observational data. So some theory might work really well for galaxies but would imply something for Cosmology that we don't observer or vice versa.

That being said, the current dark energy + dark matter model for the Universe is not completely without its own warts so modified gravity remains a possibility, albeit less likely on current evidence than the current model.

3. Oct 29, 2007

### cristo

Staff Emeritus
Are these tensor vector scalar theories the same as "f(R)" theories of which I have heard. That is, theories in which the Einstein Hilbert action of GR is changed from R to some function f(R)?

4. Oct 29, 2007

### MonstersFromTheId

Tx Wallace! That wiki article is great, but MAN have *I* got some reading to do!

5. Oct 29, 2007

### Wallace

I think they are different, but I'm very far from certain about that.

6. Oct 29, 2007

### nrqed

I think that there is some differences in the way those things are defined depending on your source. I am used to see the following definition:

Scalar tensor theories have a scalar field introduced via
$$\int d^4x \sqrt{-g} ~\bigl( \frac{f(\phi)}{2} R - \frac{\omega(\phi)}{2} \nabla^c \phi \nabla_c \phi - V(\phi) \bigr)$$

As special case of th eabove is the Brans-Dicke theory.

I am used to seeing "generalized scalar-tensor theories" defined as

$$\int d^4x \frac{\sqrt{-g}}{16 \pi} ~\bigl( f(\phi,R) - \frac{\eta}{2} \nabla^c \phi \nabla_c \phi \bigr)$$

and modified gravities as simply
$$\int d^4x \sqrt{-g} \, f(R)$$

But these are not the most general models. One can introduce functions of the Riemann tensor (as opposed to only the Ricci scalar) or the Weyl tensor and so on.

The possibilities are endless

7. Oct 29, 2007

### Wallace

Aye there's the rub. With an endless range of possible modifications it's no surprise that modified gravity is capable of solving just about any problem in cosmology. If modified gravity successfully mimics some other result how are we supposed to tell the theories apart? Maybe the LHC will save us!

8. Oct 29, 2007

### nrqed

I agree completely. Actually, it has been proven that if one simply adds a scalar (like in the scalar-tensor model I mentioned above) with an arbitrary potential, one can reproduce *any* time evolution for the scale factor!

So just adding a scalar is not interesting. But corrections in powers of R are to be expected if one thinks of GR as an effective field theory. So if one would reproduce observations (including effects such as acceleration of the expansion or drak matter effects) from higher order terms in R or the Riemann tensor, I personally think that would be interesting. well, a paper by Carroll et al on exactly that led to a large number of citations (I think) so it's not devoid of interest.

9. Oct 30, 2007

### cristo

Staff Emeritus
Thanks for highlighting the differences, nrqed.

10. Oct 30, 2007

### Garth

And that might be significant if there is indeed an age problem in the early universe. Critique of Mainstream Cosmology

Garth

11. Nov 30, 2009

### emc2cracker

I very much like the most recent theory by John Moffat. People have the misconception that this is somehow degrading to Einstiens theory, in fact I believe Einstien would be excited about this theory, he went on trying to make a similar theory.

I have a question for you math experts here. Modified gravity makes no attempt to couple the repulsive gravitational field near massive objects with electromagnetism as Einstien did. However does this mean under MOG that is not possible? I am intrigued at what MOG means for magnetar stars. I hope this theory is correct, it seems to me dark matter and energy are simply made up in order to make our current accepted gravity theory work. Seems to me this is much like the planet Vulcan prediction, just shoveling in more matter to make the math work.

I am no physicist, but I am a diligent enthusiast trying to grasp all this and study it. Professor John Moffat is kind of my role model, coming from limited educational background he is basically a self made physicist so maybe there is some hope for enthusiasts like me.

Strange this topic has been silent so long, according to the professor nothing has come in observational data within the past two years to debunk his theory. If that is so it seems it should be gathering support, but it seems it has been forgotten and disregarded.

12. Nov 30, 2009

### twofish-quant

Quite true. In fact most modified gravity theories go out of their way to avoid making any changes to gravity near massive objects. The reason for this is that there is no evidence of any odd gravitational behavior near massive objects, so all of the modified gravity theories are designed match standard gravity at short non-galactic distances.

You try to make it mean nothing. The trouble is that magnetars and anything involving magnetism are incredibly hard to model even with standard gravity. If you add strange gravitational effects, then you make it impossible to get any sort of prediction out.

Pretty much all simulations involving magentars and accretion discs use Newtonian gravity. You want to keep the gravity model dead simple since the magnetic fields and hydrodynamics end up so complicated.

It is. However it's not clear whether this is the prediction of Neptune, Vulcan, or Pluto.

That's because its one of about several dozen different theories involving modified gravity that people are looking at. There's nothing about Moffat's theory of gravity that says "pick me!!!" over the several dozen other modified gravitational theories that are in play right now. There are probably several hundred different papers on modified gravity models.

Also a lot of these observations take a lot of time and effort. There is an interaction between theorists and observationalists, because a lot of what theorists do is to come up with smoking guns for observationalists to look for.

One thing that is pretty cool to see plotted is what I call an "exclusion chart". What you do is to take a diagram, plot predictions that different models have, and as data comes in, you knock out models that don't work. The really cool part of these charts is that when it comes time to write grant proposals, you have this chart that says "look here."

13. Dec 1, 2009

### Jonathan Scott

MOND has a very nasty feature which probably creeps into most other modified gravity theories as well. It claims that the MOND-type gravitational effect on objects depends on whether the acceleration of that object (in some absolute or relative sense) is less than some threshold value. However, a macroscopic object such as a star is made up of smaller objects (atoms and molecules) which are undergoing much higher accelerations (due to the local gravitational field), which means that by the same logic they should be immune to such MOND-type accelerations. MOND supporters seem to think that this doesn't matter and assert vaguely that the motion of the star as a whole doesn't need to be determined by the motion of its constituent particles, but I don't buy that.

The reason for this postulated cut-off is because it is thought that MOND-type deviations from Newtonian or GR gravity would have been noticed by now within solar system dynamics or the laboratory.

Certainly such forces should be just about observable at a laboratory level, but because they are proportional to sqrt(m)/r instead of m/r^2, it seems likely that any standard Cavendish-type measurements would normally try to minimize them in comparison with the Newtonian forces (by maximizing m and minimizing r), and although there have been experiments to look for non-Newtonian gravitational forces, I think they have always been concentrating on even higher powers of 1/r, not lower ones. (It's well known that different experiments have given unexpectedly different values of G, so perhaps this could be a factor).

Also, such effects should now be observable from space probe orbits in the solar system, as they are of a similar order to the well-known "Pioneer anomaly". There could of course be a connection with that anomaly, but I don't personally think that the figures match at the moment.

I have therefore not yet ruled out the possibility that a MOND-like modification to gravity might still work WITHOUT any cut-off threshold, and I'd be very interested to see any experimental evidence for or against that hypothesis.

14. Dec 2, 2009

### Chronos

MOND is very unpalatable to me. With MOND you must rewrite the laws of the universe in ways consistent with observation. It might be right, but, I want to see all the rewritten laws and their consistency with observation.

15. Dec 2, 2009

### Jonathan Scott

I think that a theory which predicts the MOND effect can be derived from the assumption that a volume of space containing a fraction m/M of the mass of the universe has a surface solid angle deficit of $8 \pi m/M$, in an analogous way to angular deficits on an ordinary sphere. This has only one parameter, M, which effectively represents the mass of the universe. It effectively matches MOND when M = 2c4/Ga0 where a0 is the MOND acceleration parameter. This gives M approximately equal to 2 x 1054kg which is high but still plausible.

Edit: Couldn't get typos in Latex to go away, so converted them to text.

Last edited: Dec 2, 2009
16. Dec 2, 2009

### Wallace

The theoretical basis for MOND aside, recent evidence has gone against the phenomenology being a correct description of gravity. Some of the problems include MOND not being able to explain galaxy-galaxy strong lenses as well as not getting even close to describing galaxy merger rates and timescales observed. MOND's problems make CDM's warts look like beauty spots!

Even most of those working in MOND now accept that some amount of dark matter is needed for MOND to work. You can't yet rule out MOND + less dark matter than the CDM model needs, but you can rule out MOND with no dark mattter.

More broadly, the comparison between some kind of modified gravity on large scales and dark energy is far less settled. I think it would be a brave call to say that modified gravity in that context is ruled out, but this is a different regime to that which MOND deals with.

17. Dec 2, 2009

### twofish-quant

That is one big theoretical reason that people like LCDM. Theorists like elegant models that seem to explain completely unrelated things. If you need two theories of modified gravity to explain things at different scales, then this fails the "beauty and elegance" test.

18. Dec 2, 2009

### Wallace

There are elegant and simple modified gravity models with no more free parameters than LCDM. They still have dark matter, that's looking incresinly certain, but they address dark energy. One example is the DGP braneworlds model. It has only one free parameter, a length scale, and a simple theoretical basis (as long as you can accept higher spatial dimension...).

I believe the most recent data has shown some tension with the DGP model, so it may not stand, but there are 'elegant' alternatives to LCDM. Fundamentally though, I think even alternatives would suffer some kind of fine tuning problem analgous to LCDM, so I don't think all of LCDM's theoretical unpleasantness can be solved by invoking a different theory.

19. Dec 3, 2009

### Chronos

I'm a big LCDM fan because it was cobbled from so many different and unrelated pieces. MOND, like other unorthodox theories, attempts to beautify physics. I think physics is ugly and our universe has warts.

20. Dec 8, 2009

### emc2cracker

Thank you for the enlightening comments all,

Please allow me to expand on my notion about magnetars I was being a little too vague. I believe if we ever get to witness the actual supernova explosion that forms a magnetar we will discover Einstien was indeed correct. I believe the only reason magnetars do not collapse into black holes is because of the link of electromagnetism to the repulsive gravitational force, or the fifth force in John Moffats equations. I also believe we will discover this same force is responsible for quasar jets and probably was crucial in the formation of the universe. Now some may think that is unlikely or impossible, but the logic behind the notion is pretty strong if the math is lacking at least I have yet to see an equation to show such a notion is impossible.

And I do not see how invoking dark matter makes any long term sense. Now I am certain that dark matter exists, but I do not think it is completely undetectable mass, and I do not think it is an adequate explanation to uphold relativity as is. To me it is obvious that gravity is stronger farther away than relativity allows. Lets be realistic dark matter was never discovered, it was thought up to make our galactic simulations work without reprogramming it with new math. That was when dark matter was come up with, imagine programing relativity into a simulated universe only to discover your galaxies all flew apart. I believe I would have invented dark matter too so I can actually run some simulations, but I wouldn't go on tv preaching like science knows all when clearly that was an uh-oh moment in theoretical physics. Dark matter is a patch not a fix, I'm content with it for now until a final equation explains all the movements, and I am further convinced the final equation will have to invoke some matter that we cannot see or detect.