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Friedmann Cosmology with Rotation


Dubbelosix

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Why should an incredibly slow rotation show up in CMB data? Something surely rotating with such a slow velocity does not couple to the radiation as strongly as massive galaxies. It surely once did. But as scale increases, as rotation decays, this coupling drastically and exponentially falls off as a universe ages - the CMB doesn't show up because the bending and twisting of space with regards to its rotation is negligible. 

How slow can only be measured by the way, from measurement of dark flow in this theory. Speculating on how fast from bounds that doesn't involve these measurements, makes a hypothesis, a weak one in my eyes.

 

This is why I never answered your question of how slow. All I said was, slow enough that even the phenomenon of dark flow is disputed. 

Think of it this way, galaxies are barely coupling to the rotation itself, and those objects are massive.

Another way to see this and strengthen what I say is that according to Hoyle and Narlikar, the rotational property decays because linear acceleration takes over.  Another way to state this, is that the late universe in their model, satisfies ours because the universe appears to be expanding linearly, with only a very small, almost negligible spin. 

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Particles in space have speed limits as to how fast they can possibly move.

Think about an object one Mega parsec in radius.

do you think the outer particles won't move slower than the inner particles simply by the dynamics of a non rigid body? Ie just like a Kepler decline in galaxy rotations?

The paper provides an upper boundary as to how fast you can spin a body of non rigid matter particles without causing measurable differences.

  Thats why I dug up this paper, it provides an upper boundary so that both of us can save on the effort of calculating how slow a rotation must be before uniform rotation velocities start to show up.

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9 minutes ago, Mordred said:

Particles in space have speed limits as to how fast they can possibly move.

Think about an object one Mega parsec in radius.

do you think the outer particles won't move slower than the inner particles simply by the dynamics of a non rigid body? Ie just like a Kepler decline in galaxy rotations?

The paper provides an upper boundary as to how fast you can spin a body of non rigid matter particles without causing measurable differences.

 Particles in space have speed limits as to how fast they can possibly move.

Think about an object one Mega parsec in radius.

do you think the outer particles won't move slower than the inner particles simply by the dynamics of a non rigid body? Ie just like a Kepler decline in galaxy rotations?

The paper provides an upper boundary as to how fast you can spin a body of non rigid matter particles without causing measurable differences.

 

 

 

I certainly believe that when rotation decays significantly that any residual torsion of the galaxies in a common direction in such a slow motion much be a statement about the weakness of the coupling of the systems to the rotation of the body itself.  The galaxies are treated like dust - observable CMB radiation background disturbance would be so if the universe was significantly coupled to both matter and radiation - then when you consider the size of a single quanta of photon next to the weakly rotating dark flow phenomenon, associated in this case, to the motion of the dust in the form of galaxies, then I personally feel there are good reasons to think the CMB coupling decays before the galactic couplings totally decay.

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Well there is a related set of equations to the above, that involves the anistropy of galaxy distribution due to rotation. I will see if I can relocate the article.

Though if memory serves correct, it was am advanced Cosmology lesson plan. Have to see if I can relocate I recall Raychaudhuri was part of the calcs.

 

Lets ask a question, why would galaxy rotation be any different than a rorating universe if one ignores the placement of DM?

Quite frankly the only difference would be one of scale, yet look at the dynamics of the formation of spiral arms with regards to density wave theory.

Its not a breakdown in coupling constants when you consider the binding range of the guage bosons of a given field and the miniscule mass density ie 1 proton equivalent per cubic metre.

Far less than the effective range of the strong force, gravity at the quantum level is negligible and electromagnetically the universe is charge neutral  on average.

Did you not think Ph.Ds considered coupling strengths? That is an obvious consideration.

No the decay in velocity on rotation has everything to do with GR and speed of information exchange and simple Newtonian dynamics which leads to the Kepler equations and Kepler decline.

(primarily one can show such using virial theorem) which is a classical tbeory.

This isn't something that can be handwaved away when properly modelling our universe under rotation.

Perhaps you can answer me one question though,

With the thought that you consider galaxy rotation velocity decay as a defect of the coupling strengths.

Why did you turn down the rigid body metrics of the Godel universe?

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On 23/09/2017 at 5:41 AM, Mordred said:

 Lol I've lost count on the number of models that try to state DE isn't required. Myself over the many years I've come to realize that solving DE is an extremely tricky topic.

 At one time I constantly sought an SM related thermodynamic process to explain DE, even spent a solid 5 years attempting to do so. Thankfully I was able to disprove my attempts before pursuing publication.

I'm glad you found the other paper of interest, it peaked my interest as it provided a possible solution that corresponds to my earlier failed attempts. Granted my skills and knowledge has greatly improved since then lol to be honest I was rather dense in my own attempts. 

Anyways back to a global Universe rotation, much like lambda, I've also lost track of all the potential attempts to replace DE with rotation.

 This is the reason why I wanted a line element, I've come across so many variations of universe rotation that I've come to recognize specific models simply from their vatiations. (Simply put a time saver, I can readily derive one myself) that in and of itself is trivial.

The problem still remains as you noted on the uniformity of distribution, yes the Cosmological is a scale approximation, we all recognize that the current accepted scale where one can describe as homogeneous is roughly 100 Mpc, with very strong support to increase this to 120 to 150 Mpc. Mainly due to several extremely large LSS.

 Here is the thing, I've studied so many different models relating to DE and Godel style (short for rotation) models that unless I see serious details and work into a given model. I tend to place them on the possible backburner.

Quite frankly though as the ds^2 line element of the Godel universe is simply the FRW metric rotating on a principle axis. I fail to see where this line element is not being applied.

 

  I see no reason that if the universe is rotating that we cannot detect that rotation through mass distribution at last scattering, regardless of how short lived or how slow that rotation is. One can simply look at the hydrodamic stresses via the Ruychaudhuri equations for the stress and shear components

What has been posted thus far simply alludes to a mathematical possibility, I've lost count on those as well lol. The question remains why is there no detectable influence on mass distribution and the line element in terms of the Wordline influence. 

(please don't refer to the Planck 2012 axis of evil articles) as observational evidence. That turned out to be largely calibration errors associated with the standard dipole anistropy measurement errors due to insufficient filtering of our locality both motion and other localized influences ie radiation etc. The later Planck datasets goes into extensive detail in its calibration papers in later datasets.

(I'm positive the topic of dipole anistropy was taught in your studies) its in numerous introductory textbooks.

By the way the above reminds to too much of Polowskii's efforts to correlate a spin and torsion to the FRW metric to replace DE. 

 

 

But our situations is completely new, you say ''you think scientists haven't thought about it like a coupling?''

 

Maybe they have but certainly not in the contexts we have explored -  I just don't understand the objections of my claim in this instance - it seems more than obvious dark flow has to be something we attribute to a weak coupling on the galaxies - there is absolutely no indication it should even couple to a CMB - the fact dark flow is so slow, is evidence to that effect. 

This hasn't meant however that I didn't agree that at some point, there was an axis in the CMB. But that was when rotation and equally with it the coupling strength were many factors than what it is today. Sorry, I just don't understand the intentions of objections when I offer a perfectly good explanation.

It also only makes sense to think only the largest objects in the universe, are the last objects to couple to the rotation. 

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15 hours ago, Dubbelosix said:

 

 

I certainly believe that when rotation decays significantly that any residual torsion of the galaxies in a common direction in such a slow motion much be a statement about the weakness of the coupling of the systems to the rotation of the body itself.  .

this is the statement I am primarily discussing, please define I may be misreading your previous post

1 hour ago, Dubbelosix said:

 

 

But our situations is completely new, you say ''you think scientists haven't thought about it like a coupling?''

 

I'm asking if you think that, I know they have and do.

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That was a terribly written sentence any way with a typo, earlier was an a pad using spellcheck, not fun.

 

What the sentence meant was that when rotation decays significantly, the torsion that pulls systems like the galaxies in a common direction (is so slow),  that this in itself  is a statement about the weakness of the coupling of the rotation to the objects inside of it.

 

Galaxies are massive, and they are barely coupling to the rotation.

My argument is, that dark flow is so weak, that the CMB is behaving like there was no rotational property in the universe.

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1 hour ago, Dubbelosix said:

 

 there is absolutely no indication it should even couple to a CMB - the fact dark flow is so slow, is evidence to that effect. 

 

I disagree on this hence my suggestion to look at the papers regarding boundary conditions applied via the Christoffel connections in regards to Levi_Cevita. I am still looking for a decent coverage of Einstein Cartan but quite frankly too often they are modification papers upon it.

 I may end up using Elements of astrophysics to get into the hydrodynimic equations of rotating bodies. Then show Cartan

2 minutes ago, Dubbelosix said:

That was a terribly written sentence any way with a typo, earlier was an a pad using spellcheck, not fun.

 

What the sentence meant was that when rotation decays significantly, the torsion that pulls systems like the galaxies in a common direction (is so slow),  that this in itself  is a statement about the weakness of the coupling of the rotation to the objects inside of it.

 

Galaxies are massive, and they are barely coupling to the rotation.

My argument is, that dark flow is so weak, that the CB is behaving like there was no rotational property in the universe.

kk that makes more sense,

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If it barely couples to the galaxies, what indication is there it should couple to radiation? I can understand a CMB axis when rotation was much more significant.

Dark flow is so negligible, that the background temperatures have to be behaving as though there was no rotational properties. That's how slow it is. Only massive galaxies are the objects in the universe to couple to the slow rotation and as a theoretical statement, it is a reasonable one. 

Certainly, the way I am thinking about it, is that it actually makes sense to think, as a rotation decays, that galaxies would be the last objects in the universe to show signs of the coupling.

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higher density for one just prior to the surface of last scattering the mean free path for photons being less than 10^-32. We are dealing with hydrodynamic equations, just on a more cosmological scale.

Have you ever worked with hydrodynamic equations for astrophysics/cosmology applications?

ie have you studied Virial theory and Jeans instability ?

Here is the thing thee boundary paper I posted which is what this discussion is currently about, involves how thermodynamic characteristics of a rotating body behave using the affine connections of your Christoffels to the Kronecker delta./Levi-Cevita. This reflects upon the Baryon acoustic oscillation data with its correlation to the Sache-Wolfe effect. (Sache-Wolfe is incredibly handy to measure expansion rates) in particularly anistropies of the early and late times (two different set of equations).

The above papers have all been in regards to the connections I have been referring to....

I mentioned galaxy rotations curves in reference to the hydrodynamic equations under GR, etc etc (every field model has a correlation).

 

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Yes, hydrodynamics was the very place my studies on cosmology actually began. I know of the virial theorem very well, as it was also part of my study. Not so much Jeans instability, but of course, I have heard of it.

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So here is my question, if your familiar with Virial theorem then you have some familiarity with how it applies to equations up to page 6 of this paper we got into debating about.

https://arxiv.org/pdf/0902.4575.pdf

the first section is specifically applying virial theorem, with the correlations under GR. in terms of the four momentum etc, it has applied a cosmological term to those equations without identification of cause of the terms. It gives the applicable geodesic equations in B.1 and b.2. which is applicable to redshift data.

 

Why do you have a problem with the boundary conditions as applied to this paper? or rather that the establishing of a boundary condition via CMB data wouldn't be a viable option under cosmology? Your dealing with far higher densities in fact its much easier to measure potential rotation aspects under higher density (too bad about the opacity limits, make room for GW cosmology...once we develop the technical infrastructure lol). ie the fields are more strongly coupled so under GR changes take time to propogate throughout the field. Hence development of field anistropies, which will get increasingly chaotic with constructive/destructive interferences in your higher orders of approximations

You can't avoid the fact that multiparticle systems under rotation, do behave nonlinearly, they develop their own hydrodynamics in terms of flux and vorticity, which affect \rho under the stress tensor. So does spin under field theories.

When we started this thread this was the first concern raised and has been throughout this particular thread. The question of how slow a rotation is required to avoid detection of rotation is of primary concern.

Can you show something wrong with the methodology itself in the above paper?

If not then why ignore its potential of an upper boundary?

edit forgot to add: You not only have a rotation of a field, but also under commoving coordinates of an adiabatic and isentropic fluid under expansion. This will have additional affects to the rates of information exchange under the above hydrodynamics. The paper above already included this, You have an object roughly 1 Mpc in radius.

I am using just an example rather than actual CMB size, but I could get a specific example.

How how would it take a signal in a vacuum state to reach the center from the outer edge ?

How long for that same signal under the medium like properties of spacetime, as the density increases or decreases?

Why would this not apply to a multiparticle system under rotation ?

 

The above paper demonstrates that signal speed etc does apply to the CMB under rotation ( side note, the paper does not reference a specific moment of the CMB but its history, ie the CMB still exists today....)

 

 

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On 22/09/2017 at 3:07 AM, Dubbelosix said:
 

 

I'll certainly take a look,... I expect to find many differences with how other rotary models of the universe have been modelled compared to my own. For instance, I have never seen anyone other than one other scientist, speculate that dark flow could be rotation - I simply took it one step further and applied the Hoyle Narlikar model of a decaying rotation (which is rare) I have never seen anyone do this - I noticed early on if dark flow was a phenomenon linked to rotation property of a universe, then it would need to explain why rotation is slow. Think of how surprised I was to learn then, that an expanding universe naturally experiences a decay in the rotation and the natural answer was provided through such a model.

 

I will look through it, as I said, I expect to find many differences within the theory. 

Though, a formal look through this I read 

 

''In Fig. 2, some normalized 2nd-order perturbed quantities along the light path of the last scattered photons are plotted as a function of ra(η)Ω(r, η) with Ω(r, η) = Ωrota 3 (ηǫ)r 2/(r 2 ǫ a 3 (η)) and Ωrot ∼ 6 × 10−26 m. As expected, the perturbed quantities increase with the rotating speed. ''

 

Which seems related to what we are talking about. Of course, I have recognised as a rotation speeds up a background axis would be detectable.  Having a bound, is simply not good enough, you need to ask if you taking into consideration all the physics. First of all, does this bound appreciate the measure of dark flow, what is the bound of dark flow? Has anyone done that calculation? How does that bound differ from the bound given above?

 

Since my model is very specific, these questions are actually important. Also, questions of coupling of background radiation are likely to be quelled by noticing that galaxies are supermassive and barely coupling to the rotation. The paper looks very convincing, just not sure it can answer for model in any sufficient way. I need a paper, and with it, scientists who have measured dark flow as if it were a rotational property and gather bounds from that.

I want you to consider that the rotational property of the universe, is so vanishing, that we may consider it to be in its very last stages. It has to be, if dark flow really is evidence for rotational properties. 

 

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I do recall coming across dark flow models as rotation numerous times in the past. I never saved an of them except one related. That being by Nicodem Poplowskii, who applies the the ECT I mentioned above. I have a copy somewhere and will post it once I find it. He attempts to connect particle spin to torsion via field treatments, though he primarily set hiw bounds in regards to the UV limits in his metrics. IE cosmological singularities. EH etc..He also applied the above in particle physics in terms of helicity and variations in the particle states due to torsion. (wonder if he still has his website, he used to keep copies of all his papers on it)

Once you get a chance to study most the material I have been providing, (yes takes time to absorb lol) I hope you will come to realize that the metrics I have been referencing are used in a vast majority of your different toy universe rotating models..

I haven't targeted any specific rotating model, but provided some examples using those essential equations for a robust theory.

 

edit yep his website is still up. You will find these incredibly useful in modelling a rotating universe

http://math.newhaven.edu/poplawski/publications.html

 

mainly in the techniques, applicable formulas etc

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  • 1 month later...

Don't worry Mordred, I haven't forgotten about this either, I have just been taken with the toy model of gravity right now over the toy model of rotation. I also want to study my primordial fluctuation hypothesis as well again. But I've not really had more idea's (as of yet) in which way I would like to continue with this.

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  • 4 weeks later...

being edited

Note, even though I recite a paper, I have actually corrected an equation that may be a printing error

 

 

Spiral Trajectories and Extra Background Radiation Source

 

 

A quick explanation first why that third derivative in time in the Friedmann equation leads to non-conservation.

The time derivative of the Hubble radius is

[math]\frac{dR}{dt} = v = \dot{R}[/math]

Second derivative in time leads to acceleration (as would be expected say, in Friedmanns acceleration equation)

[math]\frac{dv}{dt} = a = \ddot{R}[/math]
 
Third derivative in time leads to chaotic systems and is denoted as the jerk
 
[math]\frac{da}{dt} = j = \dddot{R}[/math]
 
The suggested equation for a non-conservation in particle number located in the effective density was suggested in a form (with rotation):
 
[math]\frac{\dot{R}}{R}(\frac{\ddot{R}}{R} + \frac{kc^2}{a})= \frac{8 \pi G}{6c^2}(\frac{\rho + P}{n})\dot{n} + \omega^2 \frac{\dot{R}}{R}[/math]
 
The rotating universe (at least in the early cosmology case) coupled to the dust inside of it strongly. This causes the charged particles in spacetime to experience a circular trajectory (in which they lose energy through the loss of radiation) which is known as a cyclotron radiation, similar to how we view charged particles accelerating in spacetime giving rise to Larmor radiation - in the case of gravity, this would be due to the weak equivalence principle.
 
 
[math]m\dot{R}^2 = \frac{e^2}{6 \pi c^3} \dddot{R} + eV[/math]
 
 
In which [math]\ddot{R} \propto \dddot{R}[/math]. As noted by Arun and Sivaram, this leads to a path that is an exponentially increasing logarithmic spiral. Of course, in the context of a rotating expanding spacetime, the decaying rotational properties means that the logarithmic path too is overcome by expansion in the bigger picture. So instead of an exponential increase, the coupling of rotation to matter requires also that the coupling fall off as rotation equally decays. Such a logarithmic spiral would instead follow an exponential decay rule in accordance to the rotation which decays ~
 
 
[math]\omega = \omega_0 e^{-\lambda t}[/math]
 
 
We can see how this relates to the third derivative directly. Differentiation leads to in the spiral equation, terms that will fit the expanding and rotating Friedmann model
 

[math]2m\dot{R}\ddot{R} = \frac{e^2}{6 \pi c^3} \ddddot{R} + e\dot{V}[/math]
 

Notice, the potential difference, also known as the voltage [math]V[/math] has picked up a charge to mass ratio coefficient,
 

[math]\dot{R} \ddot{R} = \frac{e^2}{6 \pi c^3} \dddot{R} + (\frac{e}{m})V[/math]
 
 
(As it is, this matches the non-conserved form of the Friedmann equation).
 
 
We can replace the charge to mass ratio with a gyromagnetic ratio because the universes rotation, is also a classical property. This term that can replace the charge to mass ratio works only if charges in spacetime are distributed evenly. Due to spacetime homogeneity, this seems to be a fitting case. The interesting thing, the additional rotational radiation coming from these charged particles in the early universe can contribute to an exotic zoo. The high radiation densities would lead to new particles of various types. It also stands as a contributor to the background temperatures.
 
The differentiation of both the spiral trajectory equation and the Friedmann Langrangian (an equation I derived some time back) we can see how they relate as power equations
 

[math]m\dot{R}^2 = \frac{e^2}{6 \pi c^3} \dddot{R} + eV[/math]
 
[math]\rightarrow m\dot{R}\ddot{R} = \frac{e^2}{12 \pi c^3} \ddddot{R} + \frac{1}{2}e\dot{V}[/math]
 
 
 
In which the Friedmann Langrangian and the Friedmann power equations where identified as:
 
 
[math]\mathcal{L} = m\dot{R}^2 - \frac{8 \pi Gm R}{3c^2}(\rho + 3P) + mR \omega^2[/math]
 
[math]\rightarrow \mathcal{P} = m\dot{R}\ddot{R} - \frac{8 \pi Gm R}{6c^2}(\rho + 3P)\frac{\dot{R}}{R} + mR \omega \dot{\omega}[/math]
 

The rotating universe is compatible with the spiral paths taken giving rise to the extra radiation. Notice also, the differentiation of the spiral equation yields the jolt a rare symbol ever if there was one in physics [math]\ddddot{R}[/math]. Very rarely do we have to consider such derivatives but in this model, it cannot be avoided.
 
 
 
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velocity: rate-of-change of position

acceleration: rate of change of velocity

jerk: rate of change of acceleration

jounce (snap): rate of change of jerk

crackle: rate of change of jounce

pop: rate of change of crackle

lock: rate of change of pop

drop: rate of change of lock

http://wordpress.mrreid.org/2013/12/11/jerk-jounce-snap-crackle-and-pop/

the mnemonic above came from another forum if I recall, but I can't remember which one. I found it so useful to remember I wrote it down.

edit:

ah found it



Reference https://www.physicsforums.com/threads/what-is-jerk-and-jounce-conceptually.716152/

Its the only place I recall ever seeing the higher derivatives lol.

anyways here is the 4th jounce

https://en.wikipedia.org/wiki/Jounce#cite_note-PhysicsFAQ-1

I should note none of the higher ones were ever taken seriously in particular snap crackle pop and drop. So good luck finding anything on them

got lucky found snap crackle pop

https://infogalactic.com/info/Pop_(physics)

if I recall the list went higher but I can't recall past there

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Notice from my opening post, there is a force associated to the equation

 

[math]\ddot{R} = \frac{8 \pi G R}{3}\rho - \frac{d\omega}{dt} \times R - 2\omega \times \frac{dR}{dt} - \omega \times (\omega \times R)[/math]

 

In fact, this last equation is very much like the absolute acceleration (or four component acceleration equation) or an ''apparent acceleration,'' in the rotating frame. Because Newtons laws apply to the absolute acceleration, the effect that arises is a ficticious force which can be understood when mass is involved in the picture:

 

[math]m\ddot{R} = \frac{8 \pi Gm R}{3}\rho - m\frac{d\omega}{dt} \times R - 2m\omega \times \frac{dR}{dt} - m\omega \times (\omega \times R)[/math]

 

[math]F = m\ddot{R}[/math]

 

 What you are looking at is the ''force'' which is pushing the universe away from its centre, due to a proposed rotary property of the universe. Already, the acceleration term has been shown by other scientists https://arxiv.org/ftp/arxiv/papers/1111/1111.3873.pdf to satisfy the required acceleration to satisfy dark energy.

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The problem I have with this paper is its all first order perturbations which doesn't include any examination of the second order Sache Wolfe effect on the CMB. Which strikes me as not examining the studies deeply enough.

 Review the paper I previously linked in this thread on the bounds. Where it discusses the need to examine the second order perturbation.

This paper is extremely lacking in the details it would take for myself to seriously consider. Particularly since it only includes the torsion formula which would apply to second order with no examination of the second order perturbations (stress stress is missing) via the stress tensor on temperature. Then again so is shear viscosity of the four momentum

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11 hours ago, Mordred said:

The problem I have with this paper is its all first order perturbations which doesn't include any examination of the second order Sache Wolfe effect on the CMB. Which strikes me as not examining the studies deeply enough.

 Review the paper I previously linked in this thread on the bounds. Where it discusses the need to examine the second order perturbation.

This paper is extremely lacking in the details it would take for myself to seriously consider. Particularly since it only includes the torsion formula which would apply to second order with no examination of the second order perturbations (stress stress is missing) via the stress tensor on temperature. Then again so is shear viscosity of the four momentum

 

 

I don't doubt more work needs to be done, but understanding rotation as part pf the Poincare group, it feels natural to suggest this as a theory and maybe even taken seriously in some circles that understand a more global impact for the dark flow phenomenon.

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I think the coupling of the universe to matter (exponentially drops) with size. 

 

I think the coupling ratio to the size of the universe today should be a rough but good estimate for the dark flow. The universe, is so many magnitudes greater than it was once considered and even now, cosmologists are actually quick to recognise that there could be many magnitudes of space outside the observable horizon. At least, Susskind has mentioned  at least once that the universe is many orders of magnitude greater than we had perceived. He is also open to the idea that the universe also may not actually be spatially flat and over time we will ''detect a small curve'' in the evolution of galaxies. 

 

I point out a problem with the current acceleration model which should expose something ''fundamentally wrong with our theory'' in light that dark matter is ultimately superfluous. The ratio of critical to observed energy densities, as I have mentioned a few times (which you will be aware of Mordred), is many magnitudes off, (emphasise, the use of the word, many). Something appears to be wrong within the theory. Accepting dark matter corrections, it seems the problem is inherent in the equations as a matter of the geometry of the universe. And quite frankly, there has to be some overall influence of the gravity distribution in the universe - though the matter-energy ratio content is 1% next to the background space, it still means the stress energy tensor has to be non-zero. This should in the end translate into a small curve through time. 

 

Dark flow is terribly slow today - the rate at which it actually flows is so slow, that it has been disputed a number of times. This is a testament to the dynamics involved here: A loose grip of the coupling of rotation to matter doesn't need to have happened that long ago. But evidence to me suggests that it happened a while ago when the universe did in fact become exponentially large - but this exponential growth was subsequent to the exponential decay rate of rotation due to linear expansion, as suggested and proven by Hoyle and Narlikar. The final result, maybe surprisingly in such a universe, is that a rotary property may still be observable. But the fact the universe is many times more than the order for gravitational collapse suggests that the continued ''acceleration'' may be seen in terms of a cosmological consequence of Newtons first law. 

 

This means we would have it entirely backwards concerning dark energy - we would be using it to explain the dynamics today when the universe today can be understood as continuing acceleration because the rotary property of the universe provided enough initial rotation energy to push it out of the dense Planck region and out of the critical collapse density. The rotation was probably fully responsible for this, if it is a true property of the universe. 

Another important realisation is that the rotary energy required to do this, does explain why there is so little of the stuff in the universe as it is. It takes energy to do this, so there is a bulk to horizon transfer of energy in terms of an angular component to a universe.

 

An interesting relativistic question which arises often is, ''if the universe is rotating what is it rotating relative to?''

 

I ask, ''what stops it rotating relative to itself?''

 

Another important realisation is that the archaic models of temperature and energy transfer involves systems outside other systems to allow a ''transfer of heat or energy'' into or even out of a system. The universe is a complicated system though, subject to its own laws in various forms which does not necessarily conserve this kind of classical model of heat/energy transfer. Two different situations highlight this problem, for instance, Carrol has demonstrated verbally that the appearance of new spacetime from expansion should indicate a variation of the metric tensor. Fundamentally, this investigation led to a reasoning for this, but I did not find one in the fluctuations over spacetime unless a significant curvature was involved (since this allowed a non-zero value for/over the forth power of the momenta of virtual particles). 

 

So maybe, vacuum contribution to spacetime was only significant when there was a significant curvature in the past of the universe. 

 

 

I know, there is a lot of speculations going on here. But we are hitting new territory, (in a sense) since we are using a new kind of model here. The new aspects arises from our reformulation in a logical way, concerning the true (or absolute acceleration) of a universe. If initially, I had no concept of dark energy, I would look to the classical equations to answer why a universe accelerates at all. In this instance, it leads to the intrinsic centrifugal pseudo force field. 

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On one thing we agree, the ever so slight curvature of the datasets can support a far larger universe with a curvature term that would support a closed universe. 

A paper from the South Pole observatory (can't recall the name, did a set of calculations that if expansion were to stop it would take roughly 880 Billion years to follow this curvature to return to the origin.

Where we will continue to disagree is that my view is any rotation must be detectable via CMB data ie the Sache Wolfe effect through hydrodynamic flows. This would include Dark flow, any flow of a fluid causes temperature anistrophies.

 You already know this as it is a consequence of basic entry hydrodynamics via thermodynamic friction terms which correspond to the stress viscosity and stress vorticity terms of the energy momentum stress tensor.

 This is the terms my paper discusses while yours didn't cover. So as there is viability on both views, I would still consider the upper constraints in my support paper, which goes into a more thorough examination to be more accurate than the constraints in your support paper.

However lets be clear here I don't feel either paper has fully examined the conjecture completely enough to be fully conclusive on the constraints both are lacking in my opinion. It would have been been nice to see the Monte Carlo's datasets that actually correlates to the early and late time Sache_Wolfe provided within either paper.

ie

https://arxiv.org/pdf/astro-ph/0205436.pdf

though this paper isn't addressing rotation specifically.

This paper however does address rotation effects on shear stress with Monte Carlo and hydrodynamics.

Far surpassing both of our prior papers in terms of rotation vs DE...

https://arxiv.org/pdf/1608.07961.pdf

This is the kind of paper that counts, the others merely show the viability this provides  a detailed examination included. LOL I should have remembered how handy Monte Carlo data-sets are in this previously but for some oddball reason it slipped my mind.

Here is the details on the constraints for Dark flow.

https://arxiv.org/pdf/astro-ph/0008041.pdf

"The validity of the Cosmological Principle and the isotropy it implies gained much credibility in recent years. The small fluctuations in the CMB (∆T/T ∼ 10−5 on angular scale ∼ 10◦) provide the strongest evidence that the universe can be well approximated by the FRW metric on scales larger than ∼ 1000h−1 Mpc (e.g., Peebles 1993; Wu, Lahav, & Rees 1999) On smaller scales (∼ 100h−1 Mpc) bulk flows of the order v/c ∼ 10−3 indicate that this isotropy breaks down. This is also manifested by significant correlation functions of galaxies and clusters on large scales, and structures like the Supergalactic Plane and the Great Attractor"

which was something I previously mentioned to you sometime back on thee topic of Dark flow... being a localized rather than global perturbation...

 

 

Edited by Mordred
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