Mordred

Thank you for clarifying that L is a dimensional less parameter, your age calculations are off. Unfortunately the calculations involve the density of matter, radiation, Lambda as well as the curvature term K. You also have to factor in how each expansion contributor evolves over time. the generic formula for the age of the universe is as follows (will vary depending on the applied cosmological parameters.) \[dt=\frac{da}{aH_o}\frac{1}{[\Omega_r(\frac{a_o}{a})^4 \Omega_m(\frac{a_o}{a})^3 \Omega_k(\frac{a_o}{a})^2 \Omega_\Lambda(\frac{a_o}{a})]^2}\] for our universe with K=0 and being Lambda dominant today this simplifies to \[t_o=\frac{2}{3}\frac{1}{H_O}\sqrt{\Omega_\Lambda}\sinh^{-1}\sqrt{\frac{\Omega_\Lambda}{1-\Omega_\Lambda}(\frac{a}{a^3})^3}\] How to determine the decoupling time for the CMB is a lengthy process involving the Saha equation however for out universe without going into all the required decoupling chains etc the solution simplifies to \[t_{dec}=\frac{2}{3H_O (1+z_{dec})^{3/2}}\] quite frankly the only way to truly test your theory out is to see if you can generate the same curves that the FLRW metric does You can't afford to guess at those ratios of change as the expansion history and subsequently how each factor above evolves will depend on the evolution of each of the contributors above. The Cosmological calculator in my signature will greatly help generate a dataset for you using whichever cosmological parameters you choose. Unless you can produce each curve then your theory still requires significant work. It does anyways as you still need to prove it can prove how the universe seems to expand. You also haven't recognize that we don't rely on redshift and luminosity distance. We also use methods such as intergalactic parallax.

Proton is a bit of a tricky devil as it revolves on the valence quarks two up and one down with a quark sea of indeterminant number of other quarks. Think of it as a quark gluon confined cloud

No G would not be different. Yes DM would likely be affected by Kerr metric frame dragging as it is affected by gravity just as any other particle. However it still won't clump in the same manner as baryonic matter due to lack of other field interactions such as the EM field.

One of the problems of the particle view is the electron spin taking the diameter that NTuft provided. The electrons angular momentum and that diameter. The electron angular momentum would end up exceeding the speed of light. If I recall the calculation correct it would be roughly 10 times c. The field excitation view with the increased radius this isn't the case. I mention this as it's one of the common arguments you will find that is used to support the field excitation view. Though certainly not the only argument. I should further mention that electron spin is intrinsic. It requires a 720 degree rotation to return to its original state so don't think of particles as little spinning balls.

Math is a requirement to make testable predictions. Any model for physics is literally useless if it cannot be tested.

The gravity effect only has the potential to reach into infinite range if the mass is infinite. For a BH the range that the gravity has a measurable effect is what's involved. That can determined by the r^2 relation.

lets take this equation ask yourself what units is z ? (cosmological redshift equation) \[z = \frac{\lambda_r}{\lambda_e} - 1\] now this equation is only approximtely accurate when z<1 however it will diverge into a non linear curve. The other detail to note is that -1 included. lets look at your luminosity f'/f = 1/L^4 luminosity [W/m^2] is f the flux ? even then how did you derive that given the luminosity to distance is \[D_L=\sqrt{\frac{L}{4\pi F}}\] course the one that I find truly mysterious is how you get a length from temperature. Seems to me that you've assumed each of the values are going to have the same ratio of change with the scale factor and that is not the case.

I agree @Capiertthere is absolutely no reason to have a few words on each line it makes your posts look like bad poetry please fill in the lines so everyone can actually follow what you are posting

No I posted the graphs showing non linearity. The curves themselves are not linear. I'm sure you have heard the equation y=mx+b for linear graphs? A nonlinear function is a function whose graph is NOT a straight line. Its graph can be any curve other than a straight line. Does that help You still haven't fixed your dimensions in your equations they are still invalid as a result. Convert each unit to SI units on both the LHS and RHS of the equal sign. Follow the procedure in that link I provided lets take an example \[\frac{\acute{t}}{t}=L\] so \[\frac{s}{s}= metres\] wrong does not equal the seconds are on the LHS it doesn't have units of length which are on the RHS.

The frame dragging follows the same 1/r^2 relation as that of the Newtons gravitational law

You might want to revisit your dimensional analysis.... You have in the above units units of length on the right hand side of your equations However no corresponding units of length on the left hand side in several of the above such as temperature, power, and luminosity secondly many of the above has non linear rates of change where you have linear. assuming you are dividing the primed value with the unprimed value then you have dimensionless quantities on the LHS. So the RHS definitely does not match in every case in the above. My point 5 is an example of a very distant set of measurements that can be examined using spectrographic evidence. Google Rydberg lines for what that entails. However when you account for redshift the lines show the same distance in the atomic orbitals. No you have not adequately accounted for that as your equations are too linear to handle the nonlinearity of redshift. this is what I am referring to on the nonlinearity note how Z as well as temperature suddenly spikes. Where distance now hits the x axis is the time now... previous to that is the past while to the right is the future using current cosmological parameters. You will also find that the expansion rate ie Hubble parameter is also non linear. In point of detail the above shows logarithmic rates of change. Zero on th x axis corresponds to z= 1100 CMB http://web.mit.edu/2.25/www/pdf/DA_unified.pdf use this and recheck all your equations under proper dimensional analysis

True enough considering all the different variations coordinate time, proper time, conformal time, commoving time. Though in each case it's more accurate to treat these as defined observers.

Unfortunately it does relate in one regard as a common misconception is that a higher density past equates to spacetime curvature and hence time dilation with regards to the FLRW metric. However this isn't the case there is subtle differences in curvature with regards to the FLRW metric to spacetime curvature in GR with regards to time and proper time. Anyways that's likely best left off for a different discussion.

Correct however as I mentioned above you need a cosmological term in combination to the EFE to keep the scale factor constant. Hence Einsteins blunder a static eternal solution is unstable as I mentioned previously

No in the FLRW metric if k=0 then \[T_{\mu\nu}=0\] you still have the scale factor though as that universe can still expand or contract. If the factor is constant at zero you have a static universe which is a special class of solution (Einsteins biggest blunder) and Einstein needed to add a cosmological term to get a= constant zero.

You should reexamine the FLRW metric in particular the ds^2 line element you will find the k=0 metric Euclidean which can be considered space even though the metric includes spacetime with the addition of the scale factor. Besides one of the lessons Minkowskii taught is that you cannot separate space and spacetime.

Regardless of whether your examining space or spacetime isn't doesn't matter in this case a truly flat space or spacetime can still expand or contract when you include radiation or Lambda. You can experiment with this formula which will show this \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] or use the cosmological calculator in my signature link. It will allow you to set the cosmological parameters

the point is that even if k=0 precisely the universe can still expand due to the kinetic energy terms from radiation and the cosmological constant term. A good way to understand that is to examine the single component toy model universes such as radiation or Lambda only universes alternatively the DeSitter and anti-Desitter universes. It is a good way to examine individual each comp0sition of our universe.

total energy stays constant in the FLRW metric as per an adiabatic (closed system) perfect fluid however the energy density decreases due to expansion and correlates to the cosmological redshift. The common value for number of photons is 10^{90}. That value is calculated via the Bose Einstein statistics for bosons and gives the number density of photons by setting the effective degrees of freedom at 2 for the two polarity states of the photon. For bosons chemical reactions also set to zero. Bose Einstein Statistics (bosons) \[n_i = \frac {g_i} {e^{(\varepsilon_i-\mu)/kT} - 1}\] Fermi-Dirac statistics (fermions) \[ n_i = \frac{g_i}{e^{(\epsilon_i-\mu) / k T} + 1}\] Maxwell Boltzmann (mixed ) \[\frac{N_i}{N} = \frac {g_i} {e^{(\epsilon_i-\mu)/kT}} = \frac{g_i e^{-\epsilon_i/kT}}{Z}\]

That's not quite correct, yes a critically dense universe is homogeneous and isotropic with k=0 precisely. However you can still have expansion if the kinetic energy term exceeds the potential energy term. Our universe is extremely close to flat but not only that it is still considered homogeneous and isotropic. This might surprise you but at inflation the universe was incredibly flat and well as uniform in mass distribution to the order of \[10^{15}\]. One thing to note the critical density applies the mass term with no pressure term by applying matter. The kinetic energy term isn't part of that formula. Neither is the equipment solution in the EFE for a static solution. It is the kinetic energy term that allows for expansion or contraction in a homogeneous and isotropic universe. Such as our universe. A side note tidbit the static solution is what Einstein called his biggest mistake as he attempted to add a different cosmological term to preserve the static solution. He knew the EFE also showed expansion or contraction even with a uniform mass distribution and that a static universe was inherently unstable.

You need to be careful on causal connections. Anything we can see or measure we are causally connected to in essence we are causally connected with our observable universe. I different observer at say 1000 light years away, will have a different observable universe, however would share causal connections where that faraway observers, Observable universe overlaps with ours. Causal connections don't define "now" as we receive signals from the past events. The future can also be causally connected to us from the perspective of a future observer.

Well let's replace gas with plasma. The same plasma used in star formation. Now that plasma is ionized so your dealing with a combination of rotation (conservation of angular momentum). Gravity and the EM field interactions. The EM field isn't involved for DM which is one of the distinctive differences in galaxy formation. When I get home I will find a decent article on how density wave theorem progresses but in essence the flattening into the plane is already underway with the above prior to the majority of star formation. Our galaxy for example has different star ages and also different metalicity percentages. This detail is covered in the density wave theorem.

Hint think of what a Galaxy comprises of prior to BH and stars.

Good answer +1

yes this is precisely the direction I wanted you to take, these equations are ideally suited. Good find key note on equation 5.5.4 in regards to specific acoustic impedance involving a linear, lossless wave equation.