Mordred

Your logic is not the same as my logic or Bob's logic. Logic means nothing. It's simply an aid. There is no preferred frame this is well established and if you understand the mathematics of GR with its application of invariant quantities you would understand the truth of that statement. Let's use the following math statement on the Lorentz transforms \[\mu \cdot \nu= \nu \cdot \mu)\] This statement describes the symmetric relations of the Lorentz transform.

Thats a poor excuse, one cam still stick to the math and model any form universe conditions by applying the correct math alterations provided one correctly performs the correct math operations. I can easily adapt the FLRW metric to a form that does not require a homogeneous and isotropic dstribution as per the Cosmological principle or even adapt the metric for a rotating universe. That's because I know the needed math steps. You don't learn those by simply studying pop media literature. Regardless if you study the arxiv and professional papers instead of paying attention to pop media you will learn that pop media literature makes mountains out of mole hills. Pop media will always lead a reader astray. The cosmological Principle is quite secure by observational evidence a good example is the uniformity of the CMB. The scale however one must apply is per 100 Mpc.

Ds is the separation distance interval is designated by (ct) though that's usually shortened to simply t. The interval allows time to have the same dimensionality of length via the interval

I was getting an ad barrage, just installed the Chrome adblock plus free extension and am currently seeing no ads for my phone I run Samsung internet with its adblock extension to the same results I haven't found a decent android chrome ad block extension that's free

You will never learn physics if you pay attention to interpretations which the block universe is. We don't use the block universe interpretation in actual physics. It's just an interpretation. Stick with the math involved would show

I should add the positive frequency modes are well described via any Good Dirac equations article. In case your familiar with them.

I'm start with this statement which is rather erroneous but rather than point out the mistakes I will instead describe the quantum vacuum in accordance with the mainstream. From that the errors will become more readily obvious. I will be including related formulas so may take it a bit (in case of cross posts lol). Lets start with the period prior to inflation the hot dense state. We all agree its a tiny region at an immense density and temperature. In our models we feel the energy density is roughly \[10^{19} K\]. So everything is in that thermal equilibrium state. All particles are in thermal equilibrium. At that temperature if you apply the Bose-Einstein statistics formula you will find you have roughly 10^90 photons. This is an equivalency its actually a quark/gluon plasma state other particles can exist but recall we cannot distinguish any particle species. Here is the Bose-Einstein statistic. Don't worry I don't expect anyone to be able to use these formulas. \[ n_i = \frac {g_i} {e^{(\varepsilon_i-\mu)/kT} - 1}\] In that formulas the effective degrees of freedom is 2 for photons. I gave you an article with the pertinent details earlier on. That's your low entropy state. Now lets look at the quantum vacuum including zero point energy. Were all familiar with the quantum harmonic oscillator. This was one of the earlier studies on universe from Nothing scenarios. Including Guth's original inflation which unfortunately had the effect of "Runaway Inflation". Now one of the problems you have in that quoted section is your likely not aware that when particles come into existence they have to obey numerous conservation rules. The relevant one is conservation of charge in this particular case this includes matter and its antimatter pair. For photons it is its own antiparticle the distinction lies in its circular polarization. anti-photons are Right hand polarized while photons are left hand. This rule also applies to other particles such as neutrinos. Hopefully you can see a problem with your negative and positive universe scenario. Particularly since anti matter is readily formed in numerous processes including stars. https://www.space.com/21889-solar-flares-antimatter-particles.html not to mention we collide matter particles and can can produce antimatter. Knowing that how would this correlate to you negative and positive energy universes ? Something to keep in mind, just like an electric circuit where you cannot measure voltage by placing your test leads on the same copper wire until you have a potential difference between the two lead points. One cannot determine how much energy a vacuum contains between any two coordinates with there is no difference in its potential energy. We can however look for indirect evidence Casimarr effect is one example. The main problem with the zero point energy quantum vacuum is that observations vs calculation show an error margin of 10^(120) aka the vacuum catastrophe. There are plausible solutions to this still underway. \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] lets start with the FLRW metric we wont need curvature so we can keep it set at k=0 c=1 following formulas will be in normalized units. We need to describe two field of lets go with photon/antiphoton for simplicity. Under QFT we have two operators the creation/annihilation operators. They further correspond to their propagators as well but we don't need that detail. QFT uses them to model how particles are created subsequently destroyed. This link details how it applies to the quantum harmonic oscillator aka zero point energy https://en.wikipedia.org/wiki/Creation_and_annihilation_operators#Ladder_operators_for_the_quantum_harmonic_oscillator In essence the positive and negative modes of the harmonic oscillator propagates the operators. Where the operators correspond to particle I wont go into too much detail to see if you have any comments/questions up to this point. However this is the zero point energy field and how it can give rise to particle production in essence.

An explosion has different dynamics that are measurable. You can easily confirm the difference yourself. Take a ruler from a central point at various different angles measure off 1 cm then 3 cm then 6 cm etc. Now think of the ratio of change the result of radiating outward from the central point and measure the angles. You should notice angle changes as well as a preferred direction and location. Now place dots on a balloon measure the angles prior to inflating (inflate just enough to get a sphere. Then inflate the balloon further. The angles do not change and the ratio of change in distance is identical between any two points.

It's all good I wasn't expecting you to be an expert on cosmology applications. For any post I will try to keep as much to the FLRW metric as well as supply support material on those formulas. This evening after work I will post some relevant formulas that will apply.

fair enough however there are sections of part 3 that indicate that you have a few misunderstandings in regards to universe geometry. Universe geometry doesn't describe the shape of our universe. In actuality it describes the the null geodesics due to spacetime curvature terms. Our observable universe is a sphere. However that is not its metric geometry. (Newtonian solution under GR for flat spacetime). Now this has ramifications on redshift as well as any visual observations. In point of detail spacetime curvature causes distortions. whereas flat spacetime doesn't. So we can confirm that our universe is indeed flat by studying the CMB for distortions. There is a statement in my signature. " If you wish to change the rules, you must first understand the rules." the meaning of this is that one must understand the models they wish to fix and why those models state what they do before they try to fix it. I'm positive as a physicist you can relate to that statement. Another key point is that a homogeneous and isotropic expansion can also be tested by not distance per se but just as important any changes in angles. For example let us assume expansion started at some central point radiating outward. In this scenario you would have measurable changes in angles between stellar objects as those objects move further away from the starting point. This would be an anisotropic and inhomogeneous expansion. Expansion rates would vary in locations and have a preferred direction with a preferred location. The preferred location being the starting point. You would also have varying mass density distribution. keep in mind much of this post is also to the benefit of other readers so they can also learn what is involved As many of the older forum members can tell you, I tend to try to provide as much added information as I can as well as resource links etc for those very reasons. That way everyone learns something and it has the side effect of attracting interest in a thread. I have another key policy. If a poster wishes to learn how to go about developing a model correctly and is willing to work at learning then I have no issue with doing my best to guide them in the needed formulas, lines off research or textbooks etc. Regardless if I believe their model is feasible or not. Provided that there is some measure of feasibility of course. Now I fully recognize at no point are you stating your hypothesis is correct but simply examining the feasibility. That is part and parcel of the scientific method (examine all possibilities). that being said it would be helpful to know your skills in the FLRW metric and GR. The FLRW metric itself is likely sufficient for toy model development but if you understand GR its a good step to understanding how the FLRW metric works. Thermodynamics is something you likely already know but may not be aware of how its applies in Cosmology. One further point in section 3 you describe a UCOM. I'm assuming this refers to a center of mass of the universe. If that was your intent then that would be in error. Newtons Shell theorem would apply for a uniform mass/energy distribution such as described by the Cosmological principle.

That doesn't meet observational evidence. We know that expansion is accelerating in so far as the radius of our observable universe. Might surprise you to know though that the Hubble parameter itself is decreasing over time. If the universe were in gravitational contraction this would overpower the cosmological constant which is not something that observational evidence supports. \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] this here is the critical density formula. Historically it was use to describe the point where an expanding universe would commence in collapse. This formula was derived via the equations of state for matter. The discovery of Lambda however made this equation less useful in that regard however its still used to calculate the energy density of Lambda today as we are currently in the Lambda dominant era. Lambda aka cosmological constant aka dark energy is currently the dominant contributor to expansion. In point of detail the universe was starting to slow down in expansion towards the end of the matter dominant era however Lambda turned over and started accelerating expansion. This occurred when the universe was roughly 7 Billion years old. The calculator in my signature can show the inflection point but finding it is rather a painful exercise. The precise time however will vary depending on which cosmological parameter dataset is being used

As your new to the site Be aware your restricted to 5 posts on the first day. After that the number of posts/day is unlimited. I was gathering an article you will find useful in regards to early universe entropy as well as cosmology in general as its in a textbook style. Particle Physics of the Early Universe Uwe-Jens Wiese Institute for Theoretical Physics Bern University http://www.wiese.itp.unibe.ch/lectures/universe.pdf see section 4.2 with regards to how entropy is calculated in |Cosmology applications Inflationary models commonly use the inflaton which is a quasi-particle placeholder. However a lot of modern research is leaning towards Higgs inflation this includes Allen Guth as one of his recent papers ran a comparison between the inflaton and Higgs. I myself also support Higgs inflation however I never push personal feelings as to a preference. I'm not sure what you mean by mass contracting however the mass/energy density distribution is commonly understood via the equations of state (cosmology). https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) with this we can further detail the evolution of said components as the universe expands. Those details are also in the link. I should further note the BB isn't a kinetic type explosion but a rapid spacetime expansion caused by those ideal gas laws as well as inflation. A kinetic explosion has different measurable properties. That are not homogeneous and isotropic and cannot give an homogeneous and isotropic expansion

Quite correct. Though I am going to add some detail for the posters clarity. Lets start with time is \[10^{-43}\] seconds. The volume of the Observable universe is so miniscule that curvature loses any meaning. At the extreme hot temperatures at this time roughly \[10^{19} Gev \] all particle species will be at thermal equilibrium. As no particle species are distinguishable from one another. One can describe the this state via its temperature. As photons mediate temperature (temperature being part of the EM field) the the effective degrees of freedom is 2.

There is a particular section in the Lineweaver and Davies paper that is related to this discussion "These velocities are with respect to the comoving observer who observes the receding object to have redshift, z. The GR description is written explicitly as a function of time because when we observe an object with redshift, z, we must specify the epoch at which we wish to calculate its recession velocity. For example, setting t = t0 yields the recession velocity today of the object that emitted the observed photons at tem. Setting t = tem yields the recession velocity at the time the photons were emitted (see Eqs. A.3 & A.10). The changing recession velocity of a comoving object is reflected in the changing slope of its worldline in the top panel of Fig. 1.1. There is no such time dependence in the SR relation. Despite the fact that special relativity incorrectly describes cosmological redshifts it has been used for decades to convert cosmological redshifts into velocity because the special relativistic Doppler shift formula (Eq. 2.2), shares the same low redshift approximation, v = cz, as Hubble’s Law (Fig. 2.1). It has only been in the last decade that routine observations have been deep enough that the distinction has become significant." The First equation I posted on this thread has the terms for the corrected and currently used equation from the originally used cosmological redshift equation given below. The equation below that you see in everyday links, textbooks etc for cosmological redshift quickly becomes increasingly inaccurate at greater distances. \[1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}\] further details can be found here https://arxiv.org/pdf/astro-ph/9905116.pdf

Well you have quite a bit to go through, but one side note. As an accredited Cosmologist your really going about trying to learn cosmology in a rather haphazard manner. The reason I state haphazard is that using random google searches and subsequent articles will really twist you around a great deal of convoluted paths. My biggest suggestion is to pick up a couple of cosmology textbooks. For example the zero energy universe, while it is the most popular choice for a universe from Nothing model. Has the inherent problem in that it will only would in Euclidean spacetime. Although your statement of the universe arising from quantum fluctuations is commonly accepted. The problem with negative energy and negative mass is that those terms and applications are negative to a (and this is a very important point) NON ZERO baseline. True Negative energy and negative mass however isn't viable under GR. Though antiparticles were once thought of as one possibility. An antiparticle has the same mass density as its positive partner. We will start there for now edit I should add I can easily counter a contracting universe by simply pointing out its effect on the Blackbody temperature history of the CMB. If the universe was contracting the Blackbody temperature would be increasing and not decreasing in accordance with the ideal gas laws.

Your sort of on the right track. In cosmology we have to make certain adjustments due to expansion as well as relativity. So we have a couple of different distances. We have the commoving distance as well as the proper distance. The proper distance is the invariant distance (same for all observers). The wiki coverage isn't bad, not nearly as good as a textbook but it will do in this case. https://en.wikipedia.org/wiki/Comoving_and_proper_distances The Lineweaver and Davies article in the link below has a handy graph of both commoving distance and proper distance. page 8 https://arxiv.org/pdf/astro-ph/0402278v1.pdf below is a copy from the calculator in my signature. All calculations are in Proper distance. The row 0.000 is time now rows after that are in the future while rows previous to that is in our past up till the CMB. I can set the calculator to examine prior to that but for this purpose its unnecessary. Included is the distance to the particle horizon aka the Cosmological event horizon \[{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&Scale (a)&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&H(t) \\ \hline 1.09e+3&9.17e-4&1.09e+3&3.72e-4&6.27e-4&4.53e+1&4.16e-2&5.67e-2&8.52e-4&1.55e+6\\ \hline 7.39e+2&1.35e-3&7.40e+2&7.10e-4&1.17e-3&4.50e+1&6.09e-2&8.33e-2&1.66e-3&8.32e+5\\ \hline 5.01e+2&1.99e-3&5.02e+2&1.34e-3&2.16e-3&4.47e+1&8.91e-2&1.22e-1&3.20e-3&4.51e+5\\ \hline 3.39e+2&2.94e-3&3.40e+2&2.49e-3&3.95e-3&4.42e+1&1.30e-1&1.79e-1&6.11e-3&2.46e+5\\ \hline 2.30e+2&4.34e-3&2.31e+2&4.59e-3&7.18e-3&4.36e+1&1.89e-1&2.61e-1&1.15e-2&1.36e+5\\ \hline 1.55e+2&6.40e-3&1.56e+2&8.40e-3&1.30e-2&4.29e+1&2.74e-1&3.80e-1&2.16e-2&7.49e+4\\ \hline 1.05e+2&9.44e-3&1.06e+2&1.53e-2&2.34e-2&4.20e+1&3.97e-1&5.53e-1&4.01e-2&4.15e+4\\ \hline 7.09e+1&1.39e-2&7.19e+1&2.77e-2&4.22e-2&4.10e+1&5.70e-1&8.00e-1&7.40e-2&2.31e+4\\ \hline 4.77e+1&2.05e-2&4.87e+1&5.00e-2&7.58e-2&3.97e+1&8.14e-1&1.15e+0&1.36e-1&1.28e+4\\ \hline 3.20e+1&3.03e-2&3.30e+1&9.01e-2&1.36e-1&3.81e+1&1.15e+0&1.65e+0&2.48e-1&7.15e+3\\ \hline 2.14e+1&4.47e-2&2.24e+1&1.62e-1&2.44e-1&3.61e+1&1.61e+0&2.35e+0&4.53e-1&3.98e+3\\ \hline 1.42e+1&6.59e-2&1.52e+1&2.91e-1&4.38e-1&3.38e+1&2.23e+0&3.31e+0&8.22e-1&2.22e+3\\ \hline 9.29e+0&9.71e-2&1.03e+1&5.22e-1&7.84e-1&3.09e+1&3.00e+0&4.61e+0&1.49e+0&1.24e+3\\ \hline 5.98e+0&1.43e-1&6.98e+0&9.35e-1&1.40e+0&2.75e+1&3.94e+0&6.31e+0&2.69e+0&6.94e+2\\ \hline 3.73e+0&2.11e-1&4.73e+0&1.67e+0&2.50e+0&2.33e+1&4.92e+0&8.42e+0&4.86e+0&3.90e+2\\ \hline 2.21e+0&3.12e-1&3.21e+0&2.98e+0&4.37e+0&1.83e+1&5.69e+0&1.09e+1&8.73e+0&2.23e+2\\ \hline 1.18e+0&4.60e-1&2.18e+0&5.21e+0&7.34e+0&1.24e+1&5.71e+0&1.33e+1&1.56e+1&1.33e+2\\ \hline 4.75e-1&6.78e-1&1.47e+0&8.79e+0&1.11e+1&6.06e+0&4.11e+0&1.53e+1&2.73e+1&8.74e+1\\ \hline 0.00e+0&1.00e+0&1.00e+0&1.38e+1&1.44e+1&0.00e+0&0.00e+0&1.65e+1&4.63e+1&6.74e+1\\ \hline -3.19e-1&1.47e+0&6.81e-1&1.97e+1&1.63e+1&4.93e+0&7.23e+0&1.71e+1&7.51e+1&5.99e+1\\ \hline -5.36e-1&2.15e+0&4.64e-1&2.61e+1&1.70e+1&8.54e+0&1.84e+1&1.72e+1&1.18e+2&5.73e+1\\ \hline -6.84e-1&3.16e+0&3.16e-1&3.27e+1&1.72e+1&1.11e+1&3.50e+1&1.73e+1&1.81e+2&5.64e+1\\ \hline -7.85e-1&4.64e+0&2.15e-1&3.94e+1&1.73e+1&1.28e+1&5.95e+1&1.73e+1&2.74e+2&5.62e+1\\ \hline -8.53e-1&6.81e+0&1.47e-1&4.60e+1&1.74e+1&1.40e+1&9.55e+1&1.74e+1&4.11e+2&5.61e+1\\ \hline -9.00e-1&1.00e+1&1.00e-1&5.27e+1&1.74e+1&1.48e+1&1.48e+2&1.74e+1&6.11e+2&5.60e+1\\ \hline -9.32e-1&1.47e+1&6.81e-2&5.93e+1&1.74e+1&1.54e+1&2.26e+2&1.74e+1&9.05e+2&5.60e+1\\ \hline -9.54e-1&2.15e+1&4.64e-2&6.60e+1&1.74e+1&1.58e+1&3.39e+2&1.74e+1&1.34e+3&5.60e+1\\ \hline -9.68e-1&3.16e+1&3.16e-2&7.27e+1&1.74e+1&1.60e+1&5.06e+2&1.74e+1&1.97e+3&5.60e+1\\ \hline -9.78e-1&4.64e+1&2.15e-2&7.93e+1&1.74e+1&1.62e+1&7.51e+2&1.74e+1&2.90e+3&5.60e+1\\ \hline -9.85e-1&6.81e+1&1.47e-2&8.60e+1&1.74e+1&1.63e+1&1.11e+3&1.74e+1&4.26e+3&5.60e+1\\ \hline -9.90e-1&1.00e+2&1.00e-2&9.27e+1&1.74e+1&1.64e+1&1.64e+3&1.74e+1&6.27e+3&5.60e+1\\ \hline \end{array}}\] if your reading the correct line you will see at time now. The distance to the cosmological even horizon from our location is 46.3 Gly.

It isn't any one individual but rather the scientific community. Lets do a bit of history. The FLRW metric allows for positive, negative and flat spacetimes. \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] in the above equation k is the curvature term. Historically even after Hubble discovered the universe was expanding we still could not confirm whether or universe had curved or flat spacetime on the global mass distribution. This was a point of contention all the way up to the early 90's. We did not know the universe geometry in this aspect. However we knew that curved spacetime causes visual distortions. To understand this lets examine how those distortions would occur. If you take two parallel laser beams as the beams travel through spacetime you can have 3 results. If the beams remain parallel then the spacetime the beams travelled through is flat and have a Euclidean geometry with no overall time dilation effect. In this case you would have no distortions. However If the beams converge then you have a positive curvature and you would get distortions. The same would occur if you have negative curvature. To easily understand how this curvature affects images all one has to do is look through a convex or concave lens. Clear examples are gravitational lensing and the Einstein Ring around massive objects. How does this knowledge help up. Well we have a very handy stellar region we can use. The CMB (Cosmic microwave background). This was one of the primary goals of the COBE satellite was to use the CMB background to search for those distortions and help determine the geometry of the universe. Unfortunately the COBE images were too blurred due to not being sensitive enough to make a conclusive determination. However the WMAP images that came later were much clearer and showed no distortions caused by curved spacetime. Later on Planck also confirmed these findings. We still make use of how spacetime curvature affects images, redshift, luminosity etc to this very day. A great deal of the furthest distance that Hubble viewed was through usage of intervening gravitational lenses. In point of detail Hubble couldn't get many of its images without using gravitational lenses. We also use spacetime curvature to look for under dense and over dense regions using the Sache Wolfe effect. (this is an application of redshift). Now I want to consider one further detail. You cannot have curvature if the mass distribution is uniform. You can only get curvature by having regions with higher or lower mass densities. The reason I mention this is this is another examination. There is a relation between the luminosity and mass https://en.wikipedia.org/wiki/Mass–luminosity_relation with this tool we can further look for the mass distribution as a further confirmation. further details of universe geometry can be found here http://cosmology101.wikidot.com/universe-geometry page two further details on what effect curvature has on angles Pythagorus theorem is only accurate in flat spacetime and requires corrections in curved spacetime. http://cosmology101.wikidot.com/geometry-flrw-metric/ that is one of the effects of length contraction you mentioned above. So once again we can look for this effect.

For reference an extremely handy Feymann rules listing https://porthos.tecnico.ulisboa.pt/CTQFT/files/SM-FeynmanRules.pdf

Your idea of considering the effects of relativity in regards to expansion related measurements is something that has already been examined so take heart in that. edit I should add that one of the biggest pieces of evidence of our expanding history is its metallicity history. Factors such as the density of hydrogen, lithium etc in our evolution history. The Saha equations in the nucleosynthesis link apply there. As well as the Bose_Einstein and Fermi-Dirac statistics.

All observations are calibrated to include any relativistic effects. The evidence of expansion goes well beyond simply relativistic effects. They also go beyond those involved in cosmological redshift. These methods include those such as interstellar parallax, the various methods are collectively called the cosmological distance ladder. https://en.wikipedia.org/wiki/Cosmic_distance_ladder Physicist can never rely on any single methodology in any given observation or experiment. In order to become Robust any theory must match any number of experimental and observational evidence. As far as the Hubble contention, there is ongoing evidence supporting that our local region is under-dense which has ramifications with regards to the near and far Hubble rates. This is something not mentioned in pop medial coverage of the JW telescope findings here is the related paper https://arxiv.org/abs/1907.12402 here is a later counter paper https://arxiv.org/abs/2110.04226 I post these to show other ongoing research beyond what you see in pop media. As shown there are other possibilities for the contention that go beyond claims of LCDM being incorrect or the BB itself. One thing most people also are not aware of is that the Hubble constant evolves over time. We call it a constant strictly in the historical sense. It isn't constant over time but merely constant everywhere at a given time. It should really be treated as simply a parameter. The Hubble parameter itself is in actuality decreasing in time in our Universe evolution history. the formula as a function of redshift is given by \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] this formula accounts for how matter density, radiation density and the Cosmological constant evolves overtime and its subsequent effects on our universe expansion rates. To understand how this formula is derived you would also require the equations of state for each which are a direct result of thermodynamics under the ideal gas laws. https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) these equations of state are further applied to the FLRW deceleration oft call acceleration equation. https://en.wikipedia.org/wiki/Friedmann_equations included in last link. That link also ties into the first link. You will note that relativity is inclusive the GR EFE equation used is in the Newtonian limit. Here is the route to the equation. FLRW Metric equations \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] setting \[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as \[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\] \[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\] which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0. the related GR solution the the above will be the Newton approximation. \[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] Thermodynamics Tds=DU+pDV Adiabatic and isentropic fluid (closed system) equation of state \[w=\frac{\rho}{p}\sim p=\omega\rho\] \[\frac{d}{d}(\rho a^3)=-p\frac{d}{dt}(a^3)=-3H\omega(\rho a^3)\] as radiation equation of state is \[p_R=\rho_R/3\equiv \omega=1/3 \] radiation density in thermal equilibrium is therefore \[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3 \] \[S=\frac{2\pi^2}{45}g_{*s}(at)^3=constant\] temperature scales inversely to the scale factor giving \[T=T_O(1+z)\] with the density evolution of radiation, matter and Lambda given as a function of z \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] This I already had posted on this site under a thread I currently have underway regarding nucleosynthesis in our expanding universe and an examination of the various processes as a result. https://www.scienceforums.net/topic/128332-early-universe-nucleosynthesis/ The only reason I posted this thread in Speculations is that I wish to maintain the Privilege of toy modelling. However every single formula in that thread are commonly used and are main concordance formulas.

Here is an example of how to examine Bohm Non locality with regards to Bells inequality. This is the sort of math one can apply inclusive to experimental results using said math. https://arxiv.org/pdf/1807.01568.pdf

then explain how your holonomic toroid applies and show that it is truly holonomic. While your at it you can further apply Bells inequality via the following. set a correlation function between Alice and Bobs measurement apparatus and how a measurement on Bobs apparatus does not depend on a measurement on Alice apparatus. You can use spin of electron so you should have a statement such as used in Bells inequality as \[P(A,B|a,b\lambda)=P(A,|a,\lambda|)P(B|b,\lambda)\] where\[\lambda\] is any possible hidden variable if hidden variables are involved the outcome would give \[E^(HV)(ab)=\int d\lambda f(\lambda)\bar{A}(a,\lambda)\bar{B}(b,\lambda)\]

I would suggest you examine the Bose Einstein and Fermi Dirac statistics and how it applies to blackbody temperatures in particular interest is that all effective degrees of freedom inherent in any particle species do contribute to that temperature and further allow those statistic to predict the number density of particle states at any given blackbody temperature. They are direct applications of the ideal gas laws and can work at any temperature extreme (at least until you hit a singularity state)

Look simple geometry and how you mathematically describe a triangle has little to do with your claims. You claim a Holonomic guiding wave which you call your travelling wave has an interaction that violates the maximum rate of information exchange. Referring to its hidden variable characteristic yet have not even told us what that variable is or how it would even apply to the state of a quantum system. You have event described any quantum system state. You cant even validate your travelling wave is holonomic as you claim. There is a very good reason Why Bohm himself couldn't do what you claim to do. That very reason is that the mathematics do not support your theory.

considering I hold degrees in Physics and actually understand and regularly use the mathematics of the theories you mentioned. I would suggest I understand those theories far better that you do. Hence why I have provided you the opportunity to prove me wrong. For example you cannot have a holonomic state that had any dependency on coordinates. Any state in curved spacetime would inherently have this dependency unless you can ensure translational and rotational invariance. Another related key detail is that one entangled particle does not cause a change of state in another entangled particle. Entanglement requires a correlation function, this is part of statistical mechanics. Positive, negative and no correlation has no need for any causation. a simple example is place an orange on one bag and an apple in another. Give a bag to two other people. You have a 50 % chance the bag held by Alice has an apple as well as a 50% chance its held by an orange. So the apple/orange probability state is in superposition. Once you open Alice bag that superposition state collapses as you have now determined the state and also automatically know the state in Bobs bag. If Alice had an orange then Bob can only have the apple. Particle entanglement is much the same way. In order for two particles to become entangled they must have first interacted in some fashion. An example of interaction is parametric down conversion used in entanglement experiments. Parametric down conversion further results in numerous conservation laws being applied. Conservation of energy/momentum, isospin, color, flavor, charge, lepton number etc. From these details and the experimental setup ie number and position of detectors. One then sets up a correlation function. So from this you can easily see that there is literally zero logic in trying to interpret Bohmian non locality, EPR, Copenhagen interpretations with regards to any experimental evidence and ignore the mathematics of those theories.