Friedmann Cosmology with Rotation

[Dubbelosix]

It was suggested by Arun (et al.) That rotation enters the Friedmann equation like

 

[math](\frac{\ddot{R}}{R})^2 = \frac{8 \pi G}{3}\rho + \omega^2[/math]

 

[1]. see references

 

It's proposed the correct derivation is not only longer, but in this form, should have a sign change for the triple cross product. It is also apparent, no one has offered in their work a derivation other than the one implied through the Godel model. Really what is in implied by the centrifugal term is a triple cross product, is the use of the cross product terms

 

[math]\ddot{R} = \frac{8 \pi G R}{3}\rho + \omega \times (\omega \times R)[/math]

 

Even though the centrifugal force is written with cross products [math]\omega \times (\omega \times R)[/math] it is not impossible to show it in a similar form by using the triple cross product rule 

 

[math]a \times (b \times c) = b(a \cdot c) - c(a \cdot b )[/math]

 

Using [math]\omega \cdot R = 0[/math] because of orthogonality we get

 

[math]\ddot{R} = \frac{8 \pi G R}{3}\rho - \omega^2R[/math]

 

which justifies this form of writing it as well. If the last term is the centrifugal acceleration then the acceleration in the two frame is just, while retaining the cross product definition with positive sign,

 

[math]a_i \equiv \frac{d^2R}{dt^2}_i = (\frac{d^2R}{dt^2})_r + \omega^2 \times R[/math]

 

Expanding you can obtain the asbolute acceleration

 

[math]\ddot{R} = (\frac{d}{dt} + \omega \times)(\frac{dR}{dt} + \omega \times R)[/math]

 

[math]= \frac{d^2R}{dt^2} + \omega \times \frac{dR}{dt} + \frac{d\omega}{dt} \times R + \omega \times \frac{dR}{dt}[/math]

 

[math]= \frac{d^2R}{dt^2} + \omega \times \frac{dR}{dt} + \frac{d\omega}{dt} \times R + \omega \times ([\frac{dR}{dt}] + \omega \times R)[/math]

 

[math]= \frac{d^2R}{dt^2}_r + \frac{d\omega}{dt} \times R + 2\omega \times \frac{dR}{dt} + \omega \times (\omega \times R)[/math]

 

Which is the four-component equation of motion which describes the pseudoforces. This gives us an equation of motion, with using [math] \frac{d^2R}{dt^2}_r \rightarrow \frac{8 \pi G R}{3}\rho[/math],

 

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

 

Or simply as

 

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

 

In the rotating frame we have

 

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

 

Since inertial systems are only a local approximation, the inertial frame of reference here may been seen to go to zero leaving us the general equation of motion for a universe

 

[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]

 

Using the three standard identities ~

 

[math]a_{eul} = -\frac{d\omega}{dt} \times R[/math]

 

[math]a_{cor} = -2 \omega \times \frac{dR}{dt}[/math]

 

[math]a_{cent}= -\omega \times (\omega \times R)[/math]

 

we get

 

[math]\ddot{R} = \frac{8 \pi GR}{3}\rho + a_{eul} + a_{cor} + a_{cen}[/math]

 

The concept of rotation in a universe was initially explored by Godel, but we have made some progress since his day and his simple non-expanding metric. The idea the universe has a rotation was also explored by Hawking who admitted they very well could be the kind of model we associate to reality, except the rotation has to be remarkably slow. 

 

In the discovery of dark flow, it seems this could be the perfect candidate of a residual primordial rotation. It was proven by Hoyle and Narlikar that any primordial rotation would exponentially decay in an expanding universe. This is an important realization to understand how rotation in the primordial stages was allowed to be large and decayed as the scale factor of a universe increases, leaving behind presumably, something like dark flow in the observable motion of all the systems in the universe - hopefully this will be supported with further mapping of dark flow over larger quantities of systems. 

 

Even though technically speaking, the axis could not be discernible in the Godel universe, it becomes a non-problem in a late universe which experiences a decay in rotation. Arguably, dark flow is way too slow to discern any axis of evil.  For exact values on how rotation mimics dark energy (or expansion energy) please read the link below. The rotation will give rise to the classical centrifugal force, arising in a universe and pushing systems away. 

 

A good question that puzzled me for a while is, if rotation has in fact almost decayed, why is the universe still speeding up in expansion? I have come to realize the universe is exponentially many times the size it is today, so we must reconcile the tug of gravity has been overwhelmed by the acceleration of the universe, which just like Newtons law of inertia, will continue to expand, or continue to accelerate, unless hindered by something. Dark energy, if the substance exists, is believed only to become significant when a universe gets large enough. This means dark energy does not explain how a dense universe was capable of expanding out of the Planck era. Rotation does explain this, very easily and may offer solutions in which vacuum energy can be stolen by the rotational property of the universe - I call the latter, a Bulk to Rotation process, similar to Bulk to Horizon energy transfers in cosmological models. Rotation also explains chirality oreference and can explain why the universe has a ''handedness'' that may be directly related to the antimatter problem.

 

 

 

 

references

 

[1].https://www.researchgate.net/publication/51956326_Primordial_Rotation_of_the_Universe_and_Angular_Momentum_of_a_wide_rangeof_Celestial_Objects

 

https://en.wikipedia.org/wiki/Centrifugal_force

Edited September 22, 2017 by Dubbelosix

[Mordred]

I will look at this on the weekend, but even though the above metrics may be accurate one of the problems with the Godel class of universes is the preservation of homogeneous and isotropy under rotation.

Regardless of how slow that rotation is, this is a problem.

Is your line element the same for the Godel universe? You didn't provide a line element to work from in the above?

Neither does the paper you quoted, which both is missing the equation of state influences upon the FRW line element.

Edited September 22, 2017 by Mordred

[Dubbelosix]

The rotation exponentially decays. There are no non-linearities arising today. And the universe is not perfectly homogeneous. Far from it in fact.

Godels metric is outdated. There is no expansion in his metric, so you don't start from there. You start from Friedmann's equations. 

The rotation today is compatible with dark flow. The standard model cannot answer for it in any way. 

I read the paper you provided the other day... yes it ended up being related to my work in ways. 

[Dubbelosix]

Earlier I didn't have much time, so I rushed in answering.... the rotation decays due to the Hoyle-Narlikar process. They are quite famous for their paper, which shows that rotational properties become exponentially dampened as it contains increasing linear acceleration. 

Additionally, the equation of state for the Friedmann can already be established. I tend to take there is no conservation - In a Friedmann equation, to explain that there needs to be a third derivative in time, and we also take that the equation of state does not equal zero. 

It was always an unfounded, but arguably, understandable assumption that energy must remain the same, always in a universe. It may still be true, but we must understand there are processes of exchanging the early primordial bulk energy into the rotational properties of a universe, which [may] explain the vacuum energy discrepancy. It was understandable Friedmann assumed constant energy (because he may have been just aware) of the work by Noether. Later, we find out from general relativity that cosmological conservation is not a priori - and in fact, to do so requires a cosmological definition of time, something general relativity within its framework, lacks. 

I am leaning towards some very specific paths - 

 

1) That vacuum energy does not contribute to the observable energy of the universe. A cut off of fluctuations on the Planck frequency may provide reasons why their short existences influence the vacuum, so very little.

 

2) That energy varies in a number of possible ways - such as a non-conservation process of particle production in curved spaces. Interesting things happen when curvature is in the physics - not only does it imply non-conservation for early particle production,  Sakharov points out, that in present day quantum field theory, it is assumed that the energy momentum tensor of fluctuations of the vacuum and the corresponding action which are proportional to divergent integral of the forth power over the momenta of virtual particles are actually equal to zero.  However, it has been suggested that gravitational interactions could lead to small disturbances in the equilibrium and thus a finite value of the cosmological constant.That means, he is investigating a model which has a dependence of the action of the quantum fluctuations on the curvature of space.

 

3) Not all of my physics rests on the rotation, because I know that will only reach out to a select few. But I keep it as an interesting alternative to the controversial inflation theories. 

Edited September 22, 2017 by Dubbelosix

[MigL]

The standard way of determining energy conservation is summing all energy input to a given volume and comparing to the sum of energy output.
This is obviously non-sensical on a cosmological scale ( input and output from where ? )
You mention that a cosmological definition of time is required by GR. Is this requirement based on the application of Noether's theorem to cosmological time ? I do believe that is what she was working on when she developed the theorem, but it still makes no sense to me for the previously stated reason.

Same with cosmological rotation.
Are you familiar with Newton's pail ? If you spin a pail full of water, the level rises up the outer edges.
Does it still do the same is you rotate the universe around it ?
If you subscribe to the Machian view that inertia is determined by the gravitational interaction of all the far-flung mass-energy of the universe, then it will.
But we have moved away from Ernst Mach's point of view, and so rotating the universe maybe doesn't cause the water to rise along the edges.
IE an intrinsic rotation of the universe may also be non-sensical ( rotating with respect to what ? )

[Dubbelosix]

I only said general relativity theory lacks it, I didn't mean that it needs it... it may very well need it, one day, but we may not. What was meant is that conservation is not a priori so long as Wheeler de Witts equation is true concerning time. 

 

Believe it or not, but there are good reasons to think general relativity will require a definition... one such example is that the scale factor of a universe is explicitly time-dependent. And yes, to have conservation, even in relativity, you need a translation of time. However, just because there is a translation of time, still doesn't mean energy needs to be conserved - that's the troubling thing. All the physics is right in the early universe for short chaotic events. 

 

Yes, rotation produces a centrifugal force, an intrinsic one to space time that pushes the dust inside of it in an outwards motion. It's not a real force of course. 

The great thing about the input and output thing, is that this model is outdated for a self-contained universe - field theory, for instance, in curved spacetimes, may ensure particle production happens in irreversible ways. In this sense, things are changing intrinsically, without any external source to a universe. 

Carrol argues it in another way, he says if the universes metric varies as it expands, then energy must also change. 

Edited September 22, 2017 by Dubbelosix

[Dubbelosix]

New model suggests we don't need dark energy and if that is the case, it may require a modification of the Friedmann equation as an equation of motion.

 

I have provided such an avenue. Certainly not the only one, but an interesting one that does apparently fit data. 

 

https://www.sciencealert.com/this-new-model-of-the-universe-needs-no-dark-energy-and-works-just-as-well

[Mordred]

 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. 

Edited September 23, 2017 by Mordred

[Dubbelosix]

Yes I too have investigated the universe with torsion - today, the torsion is very small to correspond to the small residual rotation left over known as dark flow. 

 

I will post up on torsion in my next topic. 

By the way, the rotation axis is only a conjecture: In the Godel metric, no such axis is distinguishable. In our approach, we assume dark flow is too slow to create a divergence in the average curvature over large distances. 

[Mordred]

Well that is quite frankly an idea that one must apply a boundary condition to the rate of rotation.

This is an essential detail to cover, how slow is valid to avoid any affect on the curvature line element through the three main eras. Radiation, matter and Lambda dominant.

How slow is required to not affect the baryonic accoustic oscillations of the CMB?

How slow to avoid detection with the early and late Sachwolfe effect? if any affect on this aspect.

This is what needs addressing for your development

Edited September 23, 2017 by Mordred

[Dubbelosix]

Slow enough I think, that detection of the rotation happens to be so small, scientists have disagreed upon its existence. It [seems] to be consensus that dark flow is real so far. Dust inside the universe couples to the rotation weakly - the universe is highly dynamic inside and the slow rotation doesn't seem to be affecting it (any more) and (if it even does).

Sachwolfe effect? I guess that is some radiation background axis thing, properly the same thing. Too slow for light to couple to it.

[Mordred]

Actually if you look further the dark flow is a local group cluster flow. Albiet a large scale structure.

I don't question dark flow as being part of our LSS group, ie a movement to the great attractor.

I question the idea of dark flow on a global dynamic.

A dark flow by definition must flow so it must be detectable .

A completeness of a model requires a means of possible testability.

For example how much affect under commoving coordinates is involved on the sspects previously mentioned for a 1 degree per Gy rotation? can we simply conclude none? or do we require proving this is slow enough?

The other question to address is " What rate of rotation can replace a (by all measurement data) homogeneous and isotropic scalar field dynamic of Lambda to preserve this apparent uniformity at such a low and non evolving Lambda constant?

What rate of rotation will suffice that will match observational data of Lambda as a replacement?

Edited September 23, 2017 by Mordred

[Dubbelosix]

I agree, that more global modelling is required.

 

I have worked out the primordial spin - to match the spin today, we need an exponential decay model. I know how to construct the model, just done no numerical calculations. I have done some interesting calculations on an extra background contributor - if the particles are charged, and if early enough, the particles inside a universe behaves like it has a cyclotron radiation. That was an interesting theory from this as well.

Interestingly there is evidence our universe once rotated strongly. Mapping of the galaxies have shown about a 1 in a million chance that their spins are by accident. One solution is that the spin of galaxies coupled to the universe when it spun much faster than it did today. 

http://physicsworld.com/cws/article/news/2011/jul/25/was-the-universe-born-spinning

 

I was very skeptical of a recent investigation which stated there was no preferred direction in the universe and that the universe is perfectly homogeneous. 

It couldn't be further from the truth. A good example is that massive holes, spanning billions of light years exist in the model which cannot be account by inflation models. 

[Mordred]

Why can they not be accounted for, every physicist knows that as the universe develops you will develop larger anistropy regions. This can readily be described via Jeans instability. The question gets more complex with the associated timing of when such LSS developed compared to last scattering washout due to the supercooling and reheating stages of inflation.

[Dubbelosix]

Maybe they do. I just read on what you where talking about, and it seems reasonable. 

[Mordred]

 An aside, you may find the calculator in my signature handy. It has been incredibly useful into ny own research on the Higgs field aspects to the FRW metric.

Its graphing capabilites are extremely useful.

In relation to this thread, the H/H_0 column will be of particular use

Edited September 23, 2017 by Mordred

[Dubbelosix]

It will certainly help. its the only tedious side to all this I think. 

[Mordred]

Couldn't agree more, there is a particular set of equations I have read in the past that will prove useful.

It gives the functions associated with a rotating universe and gives the correponding affect on galaxy stress/strain aspects ie galaxy distribution via Raychaudhuri. 

Been trying to dig it back up.

You might recognize that metric, being applied to the BB showing that the BB may not be accurate as descibed. In so far as the pop media misleads it as the BB didn't occur. (gotta love pop media)

Edited September 23, 2017 by Mordred

[Dubbelosix]

Yes, I am familiar with the Raychauduri equation, inverstigated it a while back. 

Edited September 23, 2017 by Dubbelosix

[Dubbelosix]

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): 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,

 

 

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

 

 

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]

 

 

 

[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. You may remember, we also have a third derivative in time for non-conservation in the Friedmann equation. 

 

 

 

ref: https://arxiv.org/ftp/arxiv/papers/1402/1402.5071.pdf

 

(keep in mind we have fixed an error)

[Mordred]

I agree on the rarity of jolt used in the FRW.  Will look deeper into the above. Too long a day to even think straight let alone multifield dynamics under time derivitaves lol. Heads already spinning pardon the pun

Edited September 28, 2017 by Mordred

[Mordred]

There is the paper I have been looking for the constraints on rotating universe, finally found the example I have been digging for several days now.

The constraints of a rotating universe via the CMB data, on its angular monentum. Less than [latex]10^{-9}[/latex] rad per year^-1. 

Is the Universe rotating?

https://arxiv.org/abs/0902.4575

 

On 23/09/2017 at 10:43 AM, Mordred said:

Well that is quite frankly an idea that one must apply a boundary condition to the rate of rotation.

This is an essential detail to cover, how slow is valid to avoid any affect on the curvature line element through the three main eras. Radiation, matter and Lambda dominant.

How slow is required to not affect the baryonic accoustic oscillations of the CMB?

How slow to avoid detection with the early and late Sachwolfe effect? if any affect on this aspect.

This is what needs addressing for your development

in regards to this previous discussion for potentially applicable constraints.

[Mordred]

Posting this partly so I don't lose track of it as it contains a particularly useful set of related equations.

In particular the Hamilton of torsion as per Einstein Cartan theory.

 Still looking for a decent paper for Einstein Cartan, been ages since I last studied it.

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://academic.oup.com/ptp/article-pdf/60/1/167/5213215/60-1-167.pdf&ved=0ahUKEwjAr5aWiMfWAhUT0GMKHUvVC8s4ChAWCCEwAQ&usg=AFQjCNFdW8srX_g1GxSCw05jdoTY-YaPeg

 

[Dubbelosix]

A universe is not isotropic (if) dark flow exists on cosmological scales. The universe would end up having a preferred frame of direction due to rotation. I have seen scientists make bounds on the rotation before. It amuses me, because it is without  any experimental data referred to as dark flow. Hawking and Ellis show in 1973 that rotation was less than 

[math]3 \times 10^{-11}s[/math] 

of arc per century for a microwave background scattering at redshift of [math]10^3[/math]. But if the universe is truly isotropic, then there is no space for this theory. If dark flow is real though, then forget about the theoretical models working on the bounds, we have experimental means to test the speed of the drift and from it, subsequently the rotation of the universe itself, which will indeed be slow. But dark flow is exactly the type of phenomenon we really need. 

 

The fact that there is a chirality problem in galaxies showing a 1 in about a million chance, is just an added bonus. Not just because it adds evidence to rotation, but because it can solve the antimatter problem of the universe as well, if true. It doesn't help that the most recent articles that have attempted to measure the universe has stated that it is perfectly isotropic and homogeneous without any mention of dark flow. Is it honest, that papers do this kind of thing?

 

There should have at least been a mention to remain vigilant over the phenomenon.

https://link.springer.com/article/10.1023/B:ASTR.0000009412.72889.13

Edited September 28, 2017 by Dubbelosix

[Mordred]

Well those are details, you would address in your modelling.  Yes there will always be counter arguments to pretty much any theory I've ever encountered.

No theory is complete unless it can address the boundaries of its applicability. 

The mathematical treatments within these papers is what is important. Look specifically at how they arrive at their conclusions and determine the relations in particularly the Hamiltons  of in essence a U(4) guage.

 You have no idea, how often I hear of I don't agree with such and such, so they ignore the modelling methodology that went into the model detetmination. It is more often far more important to study the methodology in its determination.

Secondly these types of studies present issues you will need to address as these constraints are recognized. Regardless of whether or not a theorist agrees or disagrees with them. 

 Take Einstein Cartan for example, I'd be willing to bet 90% of any papers you read on a rotating universe will either refer to or show metrics from ECT. (any of decent calibur that is).

The CMB data will be your Achilles heel, you need to be able to address the issues in papers with regards to it and its applicable constraints. A rotation should show up in the CMB data. 

You could not address that earlier except with the argument " the universe must rotate extremely slow". I asked how slow?

That paper provides an answer you could not...

Edited September 28, 2017 by Mordred