Mordred

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?

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.

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...

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

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 in regards to this previous discussion for potentially applicable constraints.

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

I understood your direction of approach if not the reasons behind it, that is most helpful. Thank you for the additional clarification. Yes I have no issue with an attempt with approaching the initial hot dense state from a supercondensate state. I also have considered such on numerous occassions. It is a viable possibility though tricky to correctly model for numerous reasons.

That would be helpful,

In order to measure a rate of change then you need something to measure.

I tried the isn't there route at one time, back when I first started. Coincidentally I even tried its all a relativistic illusion. The equations I have tried to show you explain why the latter isn't true. Observational evidence under numerous different bodies of evidence denied the first. I literally spent two solid years trying to explain DM under virial theorem, just to get the tools to understand the NFW profile. Funny part is the dang early structure formation killed my efforts. Go figure did the same for a number of theories. For DE, well I've mentioned numerous times redshift is only a commonly recognized body of evidence, their is plenty of others without requiring redshift. (no that is not my work above) those are papers I use for references to my studies.

Hopefully you do the same for me, no matter how well one thinks he understands something.. One often finds things forgotten as well

Really I know you won't understand the math but here is the papers. DE has been my field of active research for over a decade now. Just to highlight my years studying the topic. DARK MATTER AS STERILE NEUTRINOS http://arxiv.org/abs/1402.4119 http://arxiv.org/abs/1402.2301 http://arxiv.org/abs/1306.4954 Higg's inflation possible dark energy http://arxiv.org/abs/1402.3738 http://arxiv.org/abs/0710.3755 http://arxiv.org/abs/1006.2801 The Higgs field seesaw adresses problems I've encountered over the years in a very elegant manner that I could never address in a strictly thermodynamic process involving any other SM particle or field.

Well if you understand physics as well as I do then you would know were not that far from being able to explain both DE, DM and potentially inflation.. However you won't believe in basic physics involved in those two topics so its pointless trying to explain how, with regards to SO(10) and Helicity applications via the Higgs seesaw mechanism. Just waiting for better data to confirm quite frankly in my opinion.

Math is a universal lanquage, thats why its preferred lol. Seriously though, you do let your preconceptions get in the way of correctly understanding DM, DE and other physics related topics of Cosmology. Yes it has its limits, if we answered every question what challenges are left? That does not preclude their validity for what they are designed to describe.

Well if your not interested in learning how physics works then I don't know Math is a universal lanquage, thats why its preferred lol. Seriously though, you do let your preconceptions get in the way of correctly understanding DM, DE and other physics related topics of Cosmology. Yes it has its limits, if we answered every question what challenges are left? That does not preclude their validity for what they are designed to describe.

That requires the math, not random statements valid or invalid. All statements in physics correspond to a mathematical definition within its range of applicability. That math requires following precision in adherence to the axioms set for any value or methodology. Including precision in terminology

For any future convos I always treat particles as strictly a field excitation which exhibits wave-like and point-like characteristics. Hence I focus on fields and the wave equations primarily in terms of creation/annihilation operators. Try applying constructive and destructive interference wave equations with regards to those excitations... If you understand Dirac then your already doing so lol

Its difficult enough just to measure a GW wave, but the detector design was developed based on spin 2 being the correct choice. Here is how spin 2 "Fields " work. https://www.researchgate.net/publication/51945770_Spin-2_Fields_and_Helicity if you don't have access let me know and I will get another paper

Remember we have no confirmed value for the graviton spin. We suspect spin 2 due to the dynamics of the quadrupole wave under GR. However that is only a suspicion based on correlations to the EFE and quadropole wave dynamics.

You don't require the gravition to give rise to the quadrupole nature of a GW wave which arises from the EFE treatments. Which will also correspond to spin 2 statistics. Just because a dynamic follows a certain symmetry relation does not necessarily mean a particle is involved.

It never stays simple lol.

Ok I think I know what he may be describing but will have to think about it before I go further. Particularly in regards to 8pi.

I think we may have a translation error. "in circles" as opposed to " under rotations". ie symmetry relations Please confirm. Ie linear and and angular momentum being primary examples.

Ok the professor is probably referring to matter/radiation density equality. Which is something all the above isn't addressing. If you take the FRW metric for the critical density formula, you will get a value in the same order of magnitude of the 10^-10 joules/cubic metre. However that value is a combined value of various contributors. The contributors being matter/radiation and the cosmological constant. What you have above is an assumption of strictly the scalar field without isolating the individual equations of state for matter/ radiation and the cosmological constant. Now radiation and matter will evolve while the volume increases. They will evolve at two distinct rates. The cosmological constant however will not evolve under volume changes. This will give you the gist of matter/radiation equality see the bennchmark values at the bottom which is derived with H_0 being 70 km/s/Mpc. Different H_0 values will affect these values... judging from the format I am going to take a stab that these are on regards to chapters 5 and 6 of "Introductory to Cosmology" by Barbera Ryden. In this chapter link, https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.astronomy.ohio-state.edu/~dhw/A5682/notes5.pdf&ved=0ahUKEwiqj82OkcTWAhVJ1WMKHYuOAMcQFggqMAM&usg=AFQjCNFK8DuR-vm-kyK94ROpORXBwKNVyg However that is a guess, as its one of the few textbooks that utilizes a benchmark model in its teaching methodology ( I don't want to go too far yet as equations of state and the evolution of matter/radiation with the thermodynamic laws) gets complex real fast. But here is a start point [latex]\Omega_{total}=\Omega_{matter}+\Omega_{radiation}+\Omega_{\Lambda}[/latex] The first two densities evolve differently as the universe expands while the last remains constant. As far as we have been able to determine. Here I posted this Heuristic approach to the equations of state and how they arise in another thread and also provided some details on redshift corrections involving matter/radiation equality and evolution of both at redshifts beyond Hubble Horizon. [latex]DU=pdV[/latex]. First take the first law of thermodynamics. [latex]dU=dW=dQ[/latex] U is internal energy W =work. As we dont need heat transfer Q we write this as [latex]DW=Fdr=pdV[/latex] Which leads to [latex]dU=-pdV.[/latex]. Which is the first law of thermodynamics for an ideal gas. [latex]U=\rho V[/latex] [latex]\dot{U}=\dot{\rho}V+{\rho}\dot{V}=-p\dot{V}[/latex] [latex]V\propto r^3[/latex] [latex]\frac{\dot{V}}{V}=3\frac{\dot{r}}{r}[/latex] Which leads to [latex]\dot{\rho}=-3(\rho+p)\frac{\dot{r}}{r}[/latex] We will use the last formula for both radiation and matter. Assuming density of matter [latex]\rho=\frac{M}{\frac{4}{3}\pi r^3}[/latex] [latex]\rho=\frac{dp}{dr}\dot{r}=-3\rho \frac{\dot{r}}{r}[/latex] Using the above equation the pressure due to matter gives an Eos of Pressure=0. Which makes sense as matter doesn't exert a lot of kinetic energy/momentum. For radiation we will need some further formulas. Visualize a wavelength as a vibration on a string. [latex]L=\frac{N\lambda}{2}[/latex] As we're dealing with relativistic particles [latex]c=f\lambda=f\frac{2L}{N}[/latex] substitute [latex]f=\frac{n}{2L}c[/latex] into Plancks formula [latex]U=\hbar w=hf[/latex] [latex]U=\frac{Nhc}{2}\frac{1}{L}\propto V^{-\frac{1}{3}}[/latex] Using [latex]dU=-pdV[/latex] using [latex]p=-\frac{dU}{dV}=\frac{1}{3}\frac{U}{V}[/latex] As well as [latex]\rho=\frac{U}{V}[/latex] leads to [latex]p=1/3\rho[/latex] for ultra relativistic radiation. Those are examples of how the first law of thermodynamics fit within the equations of state. There is more intensive formulas involved. In particular the Bose-Einstein statistics and Fermi-Dirac statistics

no prob looks good, just renemember a scalar field follows spin zero, while gravity follows spin 2 statistics that has been largely confirmed via G-wave detection. Won't interfere with your methodology as any orthogonal group is reducible to the unitary Hilbert spaces.