# Cosmological constant supports MOND

1. Jan 25, 2012

### jimjohnson

Does the cosmological constant support MOND?
The equation for critical density is as follows (in terms of mass rather than density):
Critical density (90.4 x e54 gm) = matter (4.1 x e54 gm) + dark matter (20.6 x e54 gm) + dark energy/cosmological constant (65.7 x e54 gm).
Most estimates for matter are in the range of e55 gm (or more) which is close to the total for matter and dark matter (2.64 x e55 gm).
Thus, dark matter may not exist and MOND may be a correct theory. Comments?

2. Jan 25, 2012

### Nabeshin

Care to cite anything for any of these numbers and claims you have made?

At any rate, MOND is, in almost all physicists' minds, a completely dead theory due to its inability to cope with the myriad of successes dark matter has had since its initial inception in galactic rotation curves (see, for example, the bullet cluster). As a simple idea, MOND was OK and plausible, but it has gotten egregiously complicated to attempt to deal with all these new phenomenon, and trying to save it reminds me of adding more epicycles to account for the motion of planets.

3. Jan 25, 2012

### jimjohnson

I agree MOND seems rather lifeless but the numbers in the equation raised a question about the amount of dak matter. Below are the assumptions which allow for dark matter,but the assumption for mass (based on 5 x e10 stars/galaxy each .6 x sun's mass)may be considerably low as my original post states.

Assumptions for critical density: Hubble constant (H) = 72 km/sec/Mpc or 2.34 x e-18/sec; volume of universe = 9.22 x e84 cm3; cosmological constant = 7.12 x e-30 (from Brian Greene’s Hidden Reality, page 337); and ratio of matter (baryonic) to dark matter is 1 to 5. majority of baryonic matter exists as stars.

Calculation of mass based on critical density : critical density = 3 x H2/(8 x pie x G) = 9.81 x e-30 gm/cm3; density of matter and dark matter = 2.69 x e-30 gm/cm3 (9.81 x e-30 minus 7.12 x e-30); density of matter = .45 x e-30 gm/cm3 (ratio of 1 to 5); mass of both matter and dark matter = 2.47 x e55gm (volume x density); mass of dark matter = 20.6 x e54 gm; and mass of matter = 4.1 x e54 gm.

Assumptions for number of stars: number of galaxies = e11; number of stars per galaxy = 5 x e10; average mass of star = .6 x e33 gm (.3 x sun’s mass).

Calculation of matter based on number of stars: matter = 5.4 x e54 gm.

Thus, using these assumptions the results are reasonably close, 4.1 to 5.4 x e54 gm for matter. When dark matter is included, 2.47 x e55 gm, the result is also close to the e55 gm, which is based on CMB splotches size (stated in Hidden Reality, page 275).

4. Jan 26, 2012

### Chalnoth

There is no estimate for baryonic matter alone that comes remotely close to the total matter in the universe.

5. Jan 26, 2012

### jimjohnson

Chalnoth, if matter and dark matter is 24.6 x e54 gm, I think there are estimates for matter ony in this range. However, in my calculation the volume is based on 13.7 lightyears for the radius. One could use 13. parsec which would give an answer 34.6 times larger for all the mass values.
In a calculation like this, which volume is logical? Thanks

6. Jan 26, 2012

### Chalnoth

Don't use total mass, period. Use density. The density is what is an actual, physical quantity. The total mass is arbitrary because it depends upon which particular volume you pick.

And our best estimates of the density of normal matter place it at about 4.5% of the total energy density of our universe.

7. Jan 26, 2012

### jimjohnson

Thanks, for some reason I did not comprehend that the total mass was directly related to volume. My objective was to show that the total mass (matter and dark matter) was about e55 gm and then reconciled this with different estimates of mass based on the number of stars. Now, I could not find a reliable source on the distribution of matter between gas and stars so the assumption is all stars and no gas. But to compute a mass from critical density, a volume is required. Anyway, using the radius of 13.7 x e9 light years, gives 4.1 x e54g gm for matter (4.5% of total). Dark matter was 20.6 x e54 gm (22.8% of total). Now for sake of argument, assume e11 galaxies each with e11 stars with an average mass of the sun 2 x e33gm. This gives 2 x e55 gm, a number close to the sum of matter and dark matter. Thus, I thought about MOND which would explain the situation.
Based on minimal response to the post, I am wondering if there any value to my objective.

8. Jan 26, 2012

### Chalnoth

No, I think you're just confusing yourself by using very different measures of total mass in the two scenarios. Using density leaves no ambiguity.

9. Jan 26, 2012

### jimjohnson

Chalnoth, thanks for your response, I know this is not as interesting as the multi universe topic. Ok, only density will be used. The equation is: Critical Density (9.81 x e-30 gm/cm3) = matter (.45 x e-30 gm/cm3) + dark matter (2.24 x e-30 gm/cm3) + dark energy/cosmological constant (7.12 x e-30 gm/cm3). For matter, the source is Hubble Space Telescope’s average stellar density of e-9 stars/ly3 or 1.18 x e-63 star/cm3. So the key variable is the average mass of a star. If it is the sun’s mass, matter density is 2.35 x e-30 gm/cm3 and the argument for MOND has support. If the average is 30% of the sun’s mass, matter density is .7 x e-30 gm/cm3 which is higher but closer to the .45 x e-30 gm/cm3 above. Does this approach sound logical?

10. Jan 26, 2012

### Nabeshin

Not at all. Even if it were the case that the observed visual matter were able to account for the majority of the baryonic mass of the universe (which, as it has been pointed out, by almost all estimates cannot), this in no way lends support to MOND. Logically, simply because theory X which attempts to explain phenomenon Z is incorrect does not mean that theory Y which attempts to explain the same phenomenon must be correct.

MOND would need to do some footwork of its own, rather than simply discrediting other theories, to gain support.

11. Jan 27, 2012

### Chronos

The 'bullet cluster' was basically an execution style head shot for MOND. There have been some weak efforts to revive MOND since that time, but, the head wound still looks fatal. I am particularly amused by the idea of MOND allowing for some amount of dark matter. 'Pa, the dang dog drug up another sasquatch bone on the porch ...'.

12. Jan 27, 2012

### jimjohnson

13. Jan 27, 2012

### jimjohnson

[QUOTE=Chronos; I am particularly amused by the idea of MOND allowing for some amount of dark matter.
I do not see the relationship of this statement to my analysis. The density equation has nothing to do with MOND, it stands alone. My linking it to MOND was speculation based on a mass density with a high, but possible, value for the mass of an average star. This then allowed for no dark matter in the equation and MOND saya no dark matter.

14. Jan 27, 2012

### Nabeshin

But you are neglecting the fact that we have a pretty good guess on what the average mass of a star is. Or more completely, we have some information on the population of stars of various types, including those less luminous stars which we cannot see, but yet we infer their total number from statistical methods. Rather than attempting to construct things yourself, you should look to see how these numbers are arrived at in the literature so you can see the errors that come with them.

15. Jan 27, 2012

### jimjohnson

I do have references for the distribution of star classes, M 73%, K 14%... Using this information and the mass of each class the average mass is .5 x mass of sun. This results in a density 2 and1/2 times what was in the density equation for mass (again using an H of 72 and the other assumptions).One other thing I noticed was that the Hubble stellar density is based on volume. I am going to rerun the numbers with a range of mass assumptions.

16. Jan 28, 2012

### jimjohnson

There are two assumptions that are wrong in the analysis contained in my original and subsequent posts.
First, to account for space expansion, the volume of universe should be 4.4 x e28 cm3. Using the critical density equation, this gives a mass for matter of 1.6 x e56 gm (rather than the .45 x e56 gm).
Second, a better estimate of the number of stars is e23 each with a mass of e33 gm (1/2 the sun). This gives a mass of e56 gm, a value close to what the critical density equation predicts.
Thus, dark matter is accounted for and the cosmological constant does not support MOND.

17. Jan 28, 2012

### juanrga

Agree with your conclusions but not with your reasoning. That MOND is a correct theory is well-established in basis to hundred of observations. Claims that MOND is dead are unfounded. MOND is well alive, but as you say DM does not exist

18. Jan 28, 2012

### Chalnoth

What are you going on about? MOND has been quite thoroughly discredited. It simply cannot come close to explaining current observational evidence, particularly cluster data and the CMB.

19. Jan 29, 2012

### juanrga

You have absolutely no idea of the topic.

20. Jan 29, 2012

### Chalnoth

As I said, MOND cannot explain the CMB, nor can it explain clusters. The bullet cluster, for example (well, technically, it can explain the bullet cluster...as long as you add some dark matter, which defeats the entire purpose of MOND).