A New Dark Matter Theory

[Edgar L. Owen]

The existence of an invisible form of matter called dark matter was first proposed to explain observational anomalies in the motion of galaxies. For example observations suggest that galaxies rotate as if they had halos of invisible mass around them because they are rotating faster than would be expected based on their apparent masses. The amount of dark matter necessary to explain the movements of galaxies is huge, about 5 times the amount of visible matter in the universe (Wikipedia, Dark matter).

 

Dark matter has been sought in the form of various types of new particles but so far none have been found. This proposal is a simple and rather obvious consequence of the Hubble expansion.

 

The Hubble expansion is an expansion of the relatively empty space between galaxies and galaxy clusters which makes up most of the universe. By contrast the space within galaxies isn’t expanding because it’s gravitationally bound by their mass (Misner, et al, Gravitation, 1973, p. 719). Thus the earth, the solar system, our galaxy, and we are not expanding but the space between galaxies is expanding. This is obviously true because if everything was expanding uniformly the expansion wouldn’t be observable.

 

The result is an uneven Hubble expansion that warps space around the boundaries of galaxies; precisely in the area that dark matter is expected to be found! And from general relativity we know that any warping of space must manifest as a gravitational effect. Thus we have a natural explanatory mechanism for the dark matter effect that involves only the expected warping of space from the uneven Hubble expansion around galaxies and doesn’t require the existence of any new particles.

 

This warping may or may not be the cause of the entire dark matter effect, but it certainly should be producing a very large gravitational effect, since the uneven expansion over the lifetime of the universe should produce a very large warping of space.

 

Distributions of dark matter can be mapped by tracing gravitational deviations of the expected paths of light beams from sources beyond them. These maps indicate a distribution of dark matter generally around galaxies but sometimes offset as well. However there is nothing to prevent these Hubble space warps, once they are created, to have a life and movement of their own. Thus dark matter distributions should initially form as halos around galaxies and galaxy clusters but then be able to move as massive objects on their own due to gravitational forces.

 

Once Hubble warps are formed they are effectively just additional areas of gravitational mass that can move through space just as galactic masses do. The continued existence of a dark matter mass is not dependent on the original galaxy it was created from. There will be a continuous creation of new dark matter warps around galaxies, but once created these can trail away and should leave detectible plumes of warping behind that reveal how galaxies moved over time.

 

Over the course of the expansion of the universe the actual effects will be extremely complex because the distribution of galactic matter with time is extremely complex. It should be fairly easy to test at least the viability of this theory by comparing the current distributions of dark and visible matter and inferring their relative motions over time and making a calculation of whether the expected warping would account for the gravitational effects of known dark matter concentrations.

 

This is one possible explanation of the dark matter effect, but not necessarily the only one. Nevertheless there should be a very substantial warping due to the uneven Hubble expansion, and that warping should be producing quite a large gravitational effect. Where is that effect if it isn’t the dark matter effect? It must be somewhere. The evidence seems quite strong and it certainly simplifies things by not requiring any new unknown types of particles.

 

This theory of dark matter also neatly explains why dark matter is dark. Not being an actual form of particulate matter it obviously doesn’t emit light. Thus it’s invisible and interacts with regular matter only via the gravitational force.

 

From my Book Relativity Made Easy, The Hidden Principles

 

Edgar

[Mordred]

Hubble warps. Have you got any of the appropriate math showing how this is possible with the thermodynamic correlations to the Einstein field equations ?. My guess is no. For one thing dark matter has an equation of state w=0.

 

Hubble constant does not have an equation of state. How do you simultaneously use a Hubble warpage to explain galaxy rotation curves which require a uniform distribution of mass (Hubble constant isn't a mass/energy value).

 

Gravitational lensing itself and early large scale structure formation using different regional values of Hubbles constant?

 

Please post your math showing how this is possible. Not your worded theory, but your mathematical proof.

 

Side note though your book Relativity made easy. Does it properly include the math of the Einstein field equations ?

 

The second side note, as the model for dark matter above is not a mainstream textbook ie taught in schools answer. This thread should belong in our Speculations forum.

 

edit: I see the moderators agree, I would like to see your light path World lines as it switches Hubble regions. By all rights you will not get anywhere close to the following Worldline.

 

[latex]d{s^2}=-{c^2}d{t^2}+a{t^2}[d{r^2}+{S,k}{r^2}d\Omega^2][/latex]

 

[latex]S\kappa,r= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}[/latex]

 

With acceleration equation relations

 

[latex]\frac{\ddot{a}}{a}=-\frac{4\pi G\rho}{3c^2}(\rho c^2+3p)[/latex]

This leads to

[latex]H^2=\frac{\dot{a}}{a}=\frac{8\pi G\rho}{3c^2}-\frac{kc^2p}{R_c^2a^2}[/latex]

 

Please show the above under your different density Hubble regions. Each Hubble region will have different refractive indexes, different light path curvature influences with significant change as it crosses your boundary conditions. Please show this, under GR the four momentum is adequate if you prefer working in the EFE as opposed to the FLRW.

 

I understand both metrics

Edited November 22, 2016 by Mordred

[Edgar L. Owen]

Mordred,

 

I think you are being arbitrary in redirecting my post.

 

1. Thorne & Misner on page 719 of Gravitation clearly state there is an uneven Hubble expansion in the areas surrounding galaxies and galaxy clusters.

2. An uneven expansion of space must clearly result in warps in the fabric of space.

3. In GR any curvature or warp in space is equivalent to a gravitational field.

4. So the Hubble warps must be producing some effect. If it isn't that attributed to dark matter what do you think it is?

5. It has 3 significant advantages as a theory of dark matter: It's in roughly the correct location, it's automatically a dark effect since no particles are producing the warping, and it requires no new unknown speculative particles. That's entirely consistent with the science.

6. Don't you think a warping of space has to have some effect, and if not dark matter then what do you propose that would be?

7. Also since space has expanded roughly 1000x since the CMB it has to be a very large effect just as the dark matter effect is known to be.

 

Edgar

[Mordred]

No but I didn't redirect your post the moderators did so.

 

Mainstream section is concordance model or understanding only not personal model ideas. I cannot help you without assessing your mathematical understanding of GR.

 

I believe I requested math not words show me your knowledge on the subject via the

Worldlines.

 

Do you understand my request?

 

We have had publishers in the past post on this forum on books they wrote about GR that had no math skill in GR. Their entire book didn't include a single equation beyond simplistic Lorentz formulas.

 

Yet they made outlandish claims without any math involved.

 

I seriously hope your not in this crowd.

Mordred,

 

I think you are being arbitrary in redirecting my post.

 

1. Thorne & Misner on page 719 of Gravitation clearly state there is an uneven Hubble expansion in the areas surrounding galaxies and galaxy clusters.

2. An uneven expansion of space must clearly result in warps in the fabric of space.

3. In GR any curvature or warp in space is equivalent to a gravitational field.

4. So the Hubble warps must be producing some effect. If it isn't that attributed to dark matter what do you think it is?

5. It has 3 significant advantages as a theory of dark matter: It's in roughly the correct location, it's automatically a dark effect since no particles are producing the warping, and it requires no new unknown speculative particles. That's entirely consistent with the science.

6. Don't you think a warping of space has to have some effect, and if not dark matter then what do you propose that would be?

7. Also since space has expanded roughly 1000x since the CMB it has to be a very large effect just as the dark matter effect is known to be.

 

Edgar

This entire post can be described as local vs a global metric. Locally the anistropy regions as they condense into LSS structures assist expansion.

 

However none of the above shows how you derive the equivalent to the NFW profile for galaxy rotation curves.

 

Nor does it show the mathematics involved in weak field lensing.

 

Did you not read my request in my first reply?

 

You wrote a book entitled " Relativity Made Easy, The Hidden Principles"

 

Showing the math should be a breeze for you. Either show the math or admit you have no math to support the claims in this post.

Edited November 22, 2016 by Mordred

[Mordred]

I agree dark matter warps spacetime just as any other form of mass. However your claim of dark matter not requiring to be of particle form but of Hubble warps is what I question.

 

"This theory of dark matter also neatly explains why dark matter is dark. Not being an actual form of particulate matter it obviously doesnt emit light. Thus its invisible and interacts with regular matter only via the gravitational force"

This is specifically what I want the math showing.

Edited November 23, 2016 by Mordred

[Edgar L. Owen]

Modred,

 

Do you think this theory is obviously incorrect? In which case I'd very much appreciate you explaining why you think so.

 

Or do you think it just needs an examination of the mathematical implications to be taken seriously? In which case I completely agree.

 

I don't see any obvious logical inconsistencies with GR that would immediately falsify it.

 

Could you please kindly explain if you think

1. Thorne and Misner are incorrect that the Hubble expansion is gravitationally bound locally?

2. Anisotropic Hubble expansion would or would not produce warps in the boundary areas?

3. Warps in the fabric of spacetime are or are not equivalent to gravitational fields?

 

Many thanks,

Edgar

[Mordred]

I think you need to examine the math involved. Both baryonic matter and DM are included in the FLRW metric under pressureless matter.

 

Hopefully you at least understand the math in GR. I still don't know. Which I will have to assume you don't know the math involved. At least until you confirm you understand the field equations.

 

The FLRW metric itself doesn't concern specifically the localized anistropy regions of the Large scale structure formation. However it does include that formation by taking into consideration their formation. The formation of LSS including the dark matter component reduces the global average density . This collapse into LSS assists expansion.

 

Now here is the problem. Dark matter and the cosmological constant is your two major mass contributors under the FLRW metric. The other player being radiation.

 

Baryonic matter contained in LSS structure formation accounts for roughly 3% of the mass budget.

 

Now here is the direct conflict with stating you do not require DM in particle form. You will end up with the wrong equation of state for dark matter. DM has equation of state w=0. It is cold which means non relativistic. Its equation of state does not add any pressure influence.

 

Which is the same treatment as baryonic matter.

 

Energy doesn't exist on its own. It is a property of particles. Just to add this caveat.

[Edgar L. Owen]

Modred,

 

Certainly the theory needs to be given a firm mathematical basis to be taken seriously. All scientific theories do.

 

However I am disappointed you are unable (or perhaps just unwilling) to provide simple answers to the very simple questions I asked above to see whether the theory is worth pursuing or not.

 

Either the uneven Hubble expansion does or does not produce warps in space which have a gravitational effect or they don't.

 

Which do you think it is? A very simple question I'd think you'd easily be able to answer.

 

Thanks,

Edgar

[Mordred]

 

 

Could you please kindly explain if you think

1. Thorne and Misner are incorrect that the Hubble expansion is gravitationally bound locally?

2. Anisotropic Hubble expansion would or would not produce warps in the boundary areas?

3. Warps in the fabric of spacetime are or are not equivalent to gravitational fields?

 

Many thanks,

Edgar

These caveats are essentially accurate, however your theory that dark matter can be explained by those caveats is not accurate.

 

How can you replace the mass term of DM by a term that requires DM to define the rate of expansion in the first place?

 

If you remove the mass of pressureless dust including dark matter you cannot define the spacetime geometry of an LSS in the first place. It is the major mass source. So your Hubble spheres cannot be defined without dark matter being treated as pressureless dust just as baryonic matter is.

 

The reason DM is difficult to detect is not because it isn't in particle form.

 

All radiation, and matter is in particle form. Matter is fermionic particles, light etc is bosonic particles So even your radiation is treated in particle form. We even treat the cosmological constant itself in particle form but in this instance its more of a placeholder. Outside of topic but you can ask clarification if you need.

 

The reason dark matter is difficult to detect is that it doesn't couple to the electromagnetic field nor the the strong force. Not because it isn't in particle form. Physicist treat every form of energy in particle form. Their equations of state determine its pressure contribution.

 

 

Now I ask you "how can you possibly state dark matter does not require particle form" when

 

a) it is cold non relativistic.

b) has all the properties best represented as fermionic as opposed to bosonic.

c) is the major contributor to mass in the LSS. Which you require to establish the gravitational structure of an LSS.

 

So how can you possibly state dark matter is due to individual Hubble spheres yet state it explains dark matter when dark matter determines those Hubble spheres in the first place?

 

That is a logical error. Your essentially stating your can explain something as non existent by a dynamic caused by the dark matter in the first place. Without DM as pressureless mass you cannot define your LSS geometry in the first place. So you cannot replace DM as due to Hubble spheres when DM defines those Hubble spheres.

 

that would be like having an effect without a cause

 

As far as DM being weakly interactive neutrinos and DM share many of the same characteristics. However neutrinos have little mass and are relativistic. A possible modern explanation for DM is "Sterile neutrinos". Both neutrinos and DM don't interact with the strong force nor electromagnetic radiation.

 

They both may interact with the weak force. All particles interact with gravity as gravity is spacetime geometry. However it is the distribution of those particles that determine the geometry in the first place. So trying to explain how the geometry accounts for DM when DM is included to determine the geometry is a logical error.

 

This is essentially how your opening post reads by analogy.

 

I can show how localized curvature not influenced by global expansion can explain dark matter. But first I need dark matter to define the local geometry.

 

Your trying to describe DM as a geometry effect but at the same time use DM to determine your geometry

Edited November 23, 2016 by Mordred

[swansont]

I think you are being arbitrary in redirecting my post.

 

 

!

Moderator Note

 

Nothing arbitrary about it. Non-mainstream science belongs in speculations. We do, however, still expect a scientific discussion, including some kind of model, evidence, or some falsifiable test that would apply to the idea.

 

 

[Edgar L. Owen]

Modred,

 

1. OK, you seem to agree that the anisotropic Hubble expansion should produce warps in the fabric of space that should have gravitational effects. So what and where are these gravitational effects if they aren't the dark matter effect? Since the universe has expanded roughly 1100 times since the CMB don't you think they should be quite significant and easily observable? So where are they if not dark matter? And since the anisotropies are produced at galactic boundaries what gravitational effect is there that isn't a dark matter effect? Can you please be kind enough to answer this simple question? Thanks....

 

2. The argument you raise in your last post roughly seems to be that in the FLRW model dark matter is a component of the expansion therefore it can't be produced by the expansion. Is that correct?

 

But this is true only in a non-iterative (time stable) system. There are numerous examples of iterative systems in which two states are functions of each other. The initial state of one system is affected by the other and in turn affects the first which in turn affects the second and so on. In fact that's generally the way things work in an time evolving universe. There are continual feedbacks among systems. So I don't see 2. as a problem unless you can make your argument clearer.

 

So I don't see any at least logical contradiction in assuming an expanding universe which produces anisotropies which in turn influence the subsequent expansion, and that this process continues in an iterative manner.

 

Thanks,

Edgar

[Mordred]

I believe I have stated my issue several times now.

 

Please show how you define DM as Hubble bubbles without DM being a particle mass.

 

Is that clear enough, as Swansont and I pointed out this requires some equations.

 

mathematically show how your theory differs from LCDM. Which does not describe the above.

I have no real issue with your descriptive of Hubble bubbles describing a localized overdense region. Though it is not a terminology I would use. I have issue with you stating this explains why we can't detect DM as it is not in particle form but due to Hubble bubbles.

 

By the way the terminology I would use is simply Gravity well as this denotes a localized inhomogeneous and anistropic metric. Where the global metric is homogenous and isotropic. (uniform).

 

Do you have the mathematical solutions describing the above ?

Edited November 23, 2016 by Mordred

[Edgar L. Owen]

Modred,

 

Again I'm disappointed you aren't willing to help me out by answering my very simple questions. I'm seriously trying to learn from you. Of course I understand the theory needs to be put on a mathematical basis to be taken seriously. But right now I'm just trying to see whether or not it's logical or not before proceeding.

 

It would be a great help if you could simply address the two points I raised in my previous post.

 

You seem to agree that there are ,"Gravity well(s) as this denotes a localized inhomogeneous and anisotropic metric within a global homogeneous and isotropic (uniform) metric."

 

I simply ask you what is the observational effect of these anisotropic local metrics in your opinion? You don't think it's the dark matter effect so how do they manifest observationally?

 

Thanks,

Edgar

[Mordred]

Well at least now we know you don't have the math supporting your theory.

 

To the last post the global vs local observational influence.

 

They manifest observationally via two seperate equations. Both while related are due to two seperate causes. Gravitational redshift vs Cosmological redshift. Both equations while they seem related are distinctly derived from two different line elements (Worldline).

This also accounts for gravitational lensing. Which by the way was my original request. I already gave the wordline for the FLRW metric above. That's your global background. Note the scale factor a(t) where t is a commoving observer. The volume change is the cause for cosmological redshift. On The local anistropy regions Galaxies etc the gravitational redshift is derived via the Newton limit solutions under GR.

The rate of large scale structure formation with dark matter can be approximated via the Jean's equation.

 

Now I have to ask Do you the math behind Worldlines in GR ?

 

Can I jump to the math? On second thought lets save time.

 

 

Tamara Davies gives a simplified coverage of both redshifts

 

 

http://www.google.ca/url?q=https://arxiv.org/pdf/astro-ph/0310808&sa=U&ved=0ahUKEwjT2JbOsr3QAhWFMGMKHU5VBDQQFggbMAM&usg=AFQjCNFE9aQDrUBHk91mW2m2K0ME7UyISQ

 

Another good paper is Hogg's

Distance measures in Cosmology

https://arxiv.org/pd...h/9905116v4.pdf.

For Newton limit

http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/Newtonian_Limit-Geodesic-Equations.htm

 

I hope your already familiar with

 

[latex]g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}[/latex]

 

I for one cannot think of a single GR introductory textbook that doesn't cover this metric It is a basic GR equation. If not let me know and we can better detail it.

 

I simply ask you what is the observational effect of these anisotropic local metrics in your opinion? You don't think it's the dark matter effect so how do they manifest observationally?

 

Thanks,

Edgar

Of course DM will have indirect observational influence. Described as pressureless matter in The Newton approximation. Key note matter being a fermionic particle. However the gravitational redshift influence is accountable and regularly done.

 

Example integrated Sache Wolfe effect. For intermediate gravity wells between the emitter and observer.

 

https://en.m.wikipedia.org/wiki/Sachs%E2%80%93Wolfe_effect

 

This can essentially model the DM influence upon observation. Ie Hubble bubble's (sounds like a bad chewing gum lol). I'll stick to gravity wells lol.

Edited November 24, 2016 by Mordred

[Edgar L. Owen]

Hi Modred,

 

We can get to the math shortly, but first help me out. I'm really seriously trying to learn here.

 

You seem to agree there are gravitational wells produced around galaxies by the Hubble expansion. My very simple question to you is why don't these gravitational wells have any gravitational effect?

 

Don't gravitational wells always have gravitational effects?

 

Thanks,

Edgar

[Mordred]

I really see your having difficulty understanding here. Of course gravity wells have gravitational effects. Why would you think otherwise?

 

That is not the issue. The issue is you cannot describe dark matter in one instant as having every characteristics of a massive particle. Which contributes to the mass of the gravity well.

 

Then on the next instant claim dark matter isn't in massive particle but an optical effect from those gravity wells.

 

That is my point. Dark matter is by every characteristics a massive particle. It does not make sense to claim gravity wells/Hubble bubbles can show dark matter as being not a massive particle.

 

Not when dark matter contributes to the gravity wells/Hubble bubbles in precisely the manner of slow moving matter identically in every sense to baryonic matter.

 

The LCDM model accounts for the optical effects due to DM's gravitational influence which has the identical equation of state as baryonic matter.

 

[latex]w=0[/latex] one care to note as DM doesn't interact via the electromagnetic force. Its temperature contribution is slightly different than say protons which has the additional degree of freedom.

 

To understand what I mean by this you need to use the Bose-Einstein/ Fermi Dirac ststistics or for non equilibrium systems the Maxwell Boltzmann equations.

 

Chapter 4.

 

http://www.wiese.itp.unibe.ch/lectures/universe.pdf:"Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

 

Ok lets do an equation of state for air molecules at room temperature. DM will actually have similar characteristics with the exception of electromagnetic interaction. Its velocity for this purpose we will assume is identical.

 

So lets set velocity of DM/air molecules at roughly 500 m/s.

 

[latex] P=w\epsilon [/latex] w is a dimensionless parameter.

 

[latex]c_s^2=\frac{dp}{d\rho}=\frac{dp}{d\epsilon}=wc^2 [/latex]

 

For non relativistic gas

[latex]P=\rho k T/\mu [/latex] where [latex]\mu [/latex] is the mean mass.

[latex]\epsilon^2=\rho c^2 [/latex]

 

so

[latex]p=\frac{kT}{c^2\mu}\epsilon[/latex]

 

[latex]w=\frac{1}{3}\frac{v^2}{c^2}[/latex]

 

if you plug 500 m/s into the last equation

[latex]w=10^{-12}[/latex] pressure is essentially zero when you plug w into [latex]w=p\epsilon[/latex]

 

So the equation of state for dark matter is identical to the equation of state for baryonic matter. All non relativistic particles have equation of state w=0 which means far less than unity 1 not exactly zero. Pressure contribution zero or extremely close to zero.

 

Let me know if you follow this so far because next I want to use that equation of state on large scale structure formation. Tying that into how LSS formation assists expansion.

 

PS its rather neat that the faster matter collapses into large scale structures the faster the universe expands.

Edited November 24, 2016 by Mordred

[Edgar L. Owen]

Modred,

 

OK, we agree that these "gravity wells" produced by the anisotropic Hubble expansion in the areas of galactic boundaries must produce actual gravitational effects.

 

So unless you can point to some other gravitational effect in those areas the dark matter effect is the obvious candidate because that's the only actually observed gravitational effect.

 

BTW I prefer the term 'Free Gravitational Fields' (FGFs) indicating distortions in spacetime not directly tied to mass concentration sources. The term 'Gravity Well' implies spherical symmetry around mass concentrations and these fields are not spherically symmetric.

 

Now as to the math.

 

The issues you raise are secondary because they have to do with consistency with other theoretical models.

 

The math that's important here is straightforward. It's simply comparing the expected forms of the FGFs with the actual distribution of DM in the real universe to see how well they corellate.

 

While this is straightforward it's complex and requires a simulation approach in which the expected development of FGFs over the age of the universe is modeled in various situations and compared with the DM distribution relative to actual galaxies.

 

There are a number of relevant issues and effects that influence the forms of FGFs:

 

1. A shepherding effect in which the surrounding dark matter tends to guide the motion of galaxies.

2. A trailing effect in which the movement of galaxies tends to leave a trail of FGFs behind it.

3. A smoothing effect in which detached FGFs tend to be smoothed out due to further Hubble expansion.

4. A reinforcing effect in which FGFs being gravitationally bound areas themselves tend to lead to strengthening along their boundaries.

5. The general effect of both galaxies and FGFs gravitationally interacting with other local galaxies and FGFs.

6. The effects of the intrinsic relative motion of galaxies and FGFs due to their gravitational interactions rather than the expansion of space.

7. A distortion effect due to the collision interactions of both galaxies and FGFs.

 

So all these must be modeled and compared against the real world distribution of DM in specific situations.

 

The other issue is of course that current maps of DM are very imprecise since DM can only be observed by gravitational lensing and its effects on surrounding visible matter.

 

So the real mathematical issue is how well do FGFs simulation models correlate with real world distributions of DM.

 

And if FGFs do correlate to DM they should provide an important additional tool for tracking the actual expansion of the universe and the motions of galaxies over the history of the universe.

 

So all in all the FGF theory of DM is quite promising because it provides a reasonable model of DM in the generally correct location based entirely on the accepted fact of anisotropic Hubble expansion, and the established fact that distortions of spacetime manifest as gravitational fields.

 

Not only that it automatically explains why DM is dark because FGFs aren't particle based.

 

Compare this with particle based theories of DM which are based entirely on 1. particles outside the standard model which are not even known to exist. 2. The extremely improbable distribution of those particles in just the right locations to account for DM.

 

From this perspective it begins to look like it's the particle based DM theories that are the 'speculative' ones.

 

Edgar

[Mordred]

I still don't understand why you haven"t posted any math to even be able to design that simulator. I've given you all the relevant equations.

 

Those equations can be adapted to practically any model. That was my purpose in posting them. Yes I gave examples of how to use them according to mainstream physics.

 

Its up to you now to use those equations and properly develop your model. Until you have the math. You do not have a model.

 

When a physicist says I have a theory. He has completed the math. He has the groundwork that allows his theory to be tested.

 

So the very fact that you claim a theory without posting the mathematical model tells me your not a scientist.

Modred,

 

OK, we agree that these "gravity wells" produced by the anisotropic Hubble expansion in the areas of galactic boundaries must produce actual gravitational effects.

 

So unless you can point to some other gravitational effect in those areas the dark matter effect is the obvious candidate because that's the only actually observed gravitational effect.

 

BTW I prefer the term 'Free Gravitational Fields' (FGFs) indicating distortions in spacetime not directly tied to mass concentration sources. The term 'Gravity Well' implies spherical symmetry around mass concentrations and these fields are not spherically symmetric.

 

Now as to the math.

 

The issues you raise are secondary because they have to do with consistency with other theoretical models.

 

The math that's important here is straightforward.

The issue I have raised is not secondary. If you perform the math you will see it is of utmost importance. How can you possibly have a free gravitational field not tied to the mass that defined the field distribution?

 

That makes no sense. You really need to start thinking in terms global vs localized. I hope but not sure you mean not tied to the Hubble flow. Which is a tethered vs non tethered galaxy. Please clarify, there is some discussion in those links I provided on tethered vs non tethered galaxies.

 

Speaking of simulations The current model is well tested via an extremely complex simulator.

 

http://www.cfa.harva...du/news/2014-10

 

http://www.illustris-project.org/

 

http://arxiv.org/ftp...5/1405.1418.pdf

 

Not only that it automatically explains why DM is dark because FGFs aren't particle based.

 

From this perspective it begins to look like it's the particle based DM theories that are the 'speculative' ones.

 

Edgar

As the particle based DM has been successfully simulated when your model has not. Your model is the more speculative.

 

You CANNOT have a free gravitational field not tied to the mass distribution.

You cannot have a gravitational effect without having a mass distribution. You cannot define a gravitational effect without having a mass distribution. You can't even define a gravitational field without its mass distribution local or global

 

You really need to sit down and actually use the equations. You don't remove the cause of the gravity well, that defines the dimensions of that well and then state the well is the source.

OK this is getting redundant. I will demonstrate proper modelling.

 

First we define the problem. We would like to see if there is a correlation between Hubble expansion and dark matter halo size as a function of cosmological redshift.

 

step two define a halo. The accepted norm is the cutoff for galaxy/halo is when the density is 200 times the critical density.

 

[latex]M=\frac{4\pi}{3}r^3_{200} 200\rho_{cr}[/latex]

 

critical density is [latex]\rho_{cr}(z)=\frac{3H^2(z)}{8\pi G}[/latex]

 

so [latex]M=\frac{100^3_{200}H^2(z)}{G}[/latex]

 

the virial velocity of the Halo is the circular velocity at the virial radius

 

[latex]V^2_{200}=\frac{GM}{r_{200}}[/latex]

therefore

[latex]M=\frac{V^3_{200}} {10H(z)}[/latex]

 

Hubble constant increases with lookback time H(z) At higher redshift the size of the halo of a given mass is smaller at a high redshift than the same mass at a lower redshift. Which makes sense as the average density of the Universe increases in the past. By the relation [latex](1+z)^3[/latex]

 

The profiles of dark matter are well simulated by the NFW (Navarro-Frenk-White profile)

 

[latex]\rho r=\frac{\rho_s}{(\frac{r}{ r_s})(\frac{1+r}{ r_s})^2} [/latex]

 

where [latex]\rho_s, r_s[/latex] are scaling parameters. when [latex]r<r_s: \rho\propto r^{-1}[/latex] when [latex]r>r_s: \rho\propto r^{-3}[/latex]

 

We can define a concentration parameter (dimensionless) as

 

[latex]\rho_s= \frac{200}{3}\rho_{cr} z \frac{c^3}{ln(1+c)-(\frac{c}{1+c})}[/latex]

 

where simulations will be needed to define the concentration index. Though the handout from one of my courses ( which is where I got this example) gives an approximate value

 

[latex]c\propto \frac{M^{-1/9}}{M_{halo-mass}}(1+z)^{-1}[/latex]

 

This example is from one of my courses, I do not know where it originated. I simply have it as a handout sheet. Might be Dr.M Franx but not positive

 

However it is a good demonstration of MODEL REQUIREMENTS. We now fill the need of having a testable model.

 

PS side note I can tell right off just looking at this we will need to adjust this at higher redshift's beyond Hubble Horizon. So this will be an approximation but not fully accurate once you start hitting the non linear portion of the scale factor. I question whether (1+z)^3 will be sufficiently accurate.

 

I would consider replacing it with [latex]z=\frac {H_0l^2}{c+\frac {1}{2}(1+q_0)H^2_0l^2/c^2+O (H^3_0l^3)}[/latex].

 

Now assuming the above tests correctly we can see that global expansion can influence in a small way the size of a DM halo. However it would follow the difference between critical density vs halo density. However I would note the possibility Without declaring the above is correct or accurate

Edited November 25, 2016 by Mordred

[Strange]

The math that's important here is straightforward. It's simply comparing the expected forms of the FGFs with the actual distribution of DM in the real universe to see how well they corellate.

 

1. You have not shown that FGFs can exist. (It appears to be impossible.)

 

2. You have not shown that they can account for the effects attributed to dark matter. As you seem to be claiming these FGFs exist at the boundaries of galactic clusters, how can they account for the dynamics within galaxies?

 

I think you need to show the detailed maths that supports points 1 and 2.

[Mordred]

 

1. You have not shown that FGFs can exist. (It appears to be impossible.)

 

2. You have not shown that they can account for the effects attributed to dark matter. As you seem to be claiming these FGFs exist at the boundaries of galactic clusters, how can they account for the dynamics within galaxies?

 

I think you need to show the detailed maths that supports points 1 and 2.

I concur and I am positive the moderators also concur as it is a speculations forum requirement.

 

http://www.scienceforums.net/topic/86720-guidelines-for-participating-in-speculations-discussions/#entry839842

6. The effects of the intrinsic relative motion of galaxies and FGFs due to their gravitational interactions rather than the expansion of space.

 

I'd like to touch on this incorrect statement. Gravitational collapse aids expansion.

 

Take a homgeneous and isotropic initial condition. As inhomogeniety occurs, the average density of matter drops, due to pooling into large sale structure formation. This means gravity has less influence on the voids away fro the LSS.

 

The very fact that gravity tends to condense into the LSS regions alone aids expansion. However we would need some rules governing LSS formation.

 

For this we will use strictly a non relativistic matter only fluid. Just matter....

 

Well one set of rules has to do with Jeans mass, Primordial density fluctuations expand linearly at a rate slower than the rate of expansion. This induces localized anistropy regions that sets up two possibilities locally. Inflow and outlfow of matter.

 

the dividing line between the two possibilities can be found by the following argument. Let the time of freefall into the overdense region be

 

[latex]t_g=1/\sqrt{G_\rho}[/latex]

 

sound waves in a medium propogate with velocity [latex]c_s=\sqrt{\frac{\partial p}{\partial\rho}}[/latex]

 

so they move one wavelength in the time

[latex]t_s=\lambda/c_s[/latex]

 

when t_g is shorter than t_s the fluctuation is unstable and will continue to grow until it collapses locally setting T_g as equal to T_s we find the Jeans instability, Which correlates the rate of expansion and collapse locally due to gravity itself (locally only)

 

[latex]\lambda_j=\sqrt{\frac{\pi}{G\rho}}c_s[/latex]

 

So we can see from this that expansion and gravity both aid in large scale structure formation. That large scale structure formation in turn helps the rate of expansion by the following equation.

 

[latex]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/latex]

 

as expansion increases and the LSS develop the matter density evolves by the ratio in the last equation. This alters the rate of expansion compared to the rate today by the last equation. You will note radaition and matter both evolve but the cosmological constant does not.

 

If you truly look and study the thermodynamics of particles, you will find nothing is more natural than an expanding or collapsing universe. Expansion is literally a thermodynamic process. (Though were still trying to fit the cosmological constant under thermodynamic process) possible solution is the Higgs metastability.

 

Essentially from the above if the matter wavelength (Jeans mass wavelength) is significantly smaller than the Hubble expansion. Locally gravity will collapse, this local collapse will in turn aid expansion by lowering the global mass density average.

[Edgar L. Owen]

Strange & Modred,

 

Well thanks for all the math guys but the crux of the argument is whether or not the anisotropic expansion of space around galactic boundaries creates warps in space or not. I think it has to.

 

And second whether or not those warps in space have gravitational effects (are equivalent to free gravitational fields). I think they have to since GR says that gravitational fields are precisely warps in otherwise flat space.

 

If this is true then we do have FGFs in the right place to be the source of the DM effect and then we can worry about the math. If it isn't true then the theory doesn't work and the math is irrelevant.

 

Edgar

[Mordred]

mass curves spacetime. This forms gravity wells. It does not form free gravitational fields as gravity is all one field. Not multiple fields. Though one can mathematically isolate systems or regions this does not mean they are not part of the global metric. The influences can influence the global metric and vise versa as I have already shown. However they remain interconnected. Not isolated.

 

I have provided two examples. One where local changes affect the global metric and one where a change in the global metric affects the local metric.

 

This shows localized gravity wells are NOT free gravitational fields. A free gravitational field is one that is isolated from the global metric. I have demonstrated in two methodologies that this is not the case. Demonstrating how localized regions are connected to the global system. Gravity wells are simply put anistropy regions under a global metric. (Global field) if you like. but they are not FREE from the Global gravitational field.

 

You cannot remove the source of the mass. Doing so changes the field curvature.

 

You have your answer. Any other declarations against the above requires math from you.

 

Oh and dark matter is in particle matter form. Not a result of free gravitational fields which by your description CANNOT exist.

 

Once again any declarations otherwise requires math from you. Otherwise this thread will end up being locked. It is a requirement in Speculations forum.

Edited November 26, 2016 by Mordred

[Klaynos]

!

Moderator Note

Currently this thread isn't meeting our minimum requirements for speculations. Please review our speculations guidelines which can be found here http://www.scienceforums.net/topic/86720-guidelines-for-participating-in-speculations-discussions/

[Edgar L. Owen]

Modred,

 

As a physics professor at a major university I'm astonished you are unable to answer the simple question of whether the anisotropic expansion of space around galactic peripheries produces warps in space that have gravitational effects or not.

 

You've continually avoided this simple question throughout the discussion.

 

Anyway thanks for your posts...

 

Best regards,

Edgar

[Mordred]

I did maybe you should spend time understanding my repeated answer to that question. Secondly I never claimed to be a professor my degree is Masters.

 

Tell me is the reason you don't understand my answer is because it conflicts with your personal theory?

 

You have been repeatably told "Of course local anistropy warps spacetime and causes gravitational effects" What do you think a gravity well is? = Spacetime warping.

 

Can I spell that out for you in any simpler terms?

 

Do you not read my posts? That IS NOT THE ISSUE. The issue is these warps are not Free gravitational fields and they DO NOT mean dark matter is not in particle form.

 

lastly what of "You must present the math to support those two assertions do you not understand"

Edited November 27, 2016 by Mordred