Mordred

\.begin{array}{rcl} a&b&c\\a&b&c\\a&b&c\end{array} \begin{array}{rcl} a&b&c\\a&b&c\\a&b&c\end{array} interesting the \begin{array} self activates f(z) = \left\{ \.begin{array}{rcl} a&b&c\\a&b&c\\a&b&c\end{array} \right . \[f(z) = \left\{ \begin{array}{rcl} a&b&c\\a&b&c\\a&b&c\end{array} \right .\]

\[\vec{v}_e+p\longrightarrow n+e^+\] \[\array{ n_e \searrow&&\nearrow n \\&\leadsto &\\p \nearrow && \searrow e^2}\]

your welcome glad to help

Correct now your getting it +1 on seeing that connection

It's a workable descriptive not completely accurate but sufficient for a layman understanding. Getting into the renormalization aspects would be a bit too advanced it's sufficient to accept that it's a renormalized value.

Well at least Chatgp got that part correct as that's precisely what it's used for. The VeV is used in a similar manner just an fyi

Here is the association of VeV to Fermi-constant Fermi's interaction - Wikipedia

A possible antineutrino cross section calculation massless case \[\vec{v}_e+p\longrightarrow n+e^+\] Fermi constant=\(1.1663787(6)*10^{-4} GeV^{-2}\) \[\frac{d\sigma}{d\Omega}=\frac{S|M|^2\acute{p}^2}{M_2|\vec{p_1}|2|\vec{p_1}|(E_1+m_2c^2)-|\vec{p_1}|\prime{E_1}cos\theta}\] Fermi theory \[|M|^2=E\acute{E}|M_0^2|=E\acute{E}(M_Pc^2)^2G^2_F\] \[\frac{d\sigma}{d\Omega}=(\frac{h}{8\pi}^2)\frac{M_pc^4(\acute{E})^2G^3_F}{[(E+M_p^2)-Ecos\theta]}\] \[\frac{d\sigma}{d\Omega}=(\frac{h}{8\pi}^2)\frac{M_pc^4(\acute{E})^2G^3_F}{M_pc^2}(1+\mathcal{O}(\frac{E}{M_oc^2})\] \[\sigma=(\frac{\hbar cG_F\acute{E}^2}{8\pi})^2\simeq 10^{-45} cm^2\] \

you won't find that equation in a textbook, textbooks only show the basic equations in math speak in this case you would usually see the first order equation this delves into the second order. just as most textbooks won't show the equation \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] this shows the expansion rate H varies over time (it will also help to better understand the first equation as well as the Hogg paper I posted. now as you mentioned DM and DE one line of research is Higgs being responsible. Sterile neutrinos (right hand are heavier than left hand neutrinos ) antimatter and matter neutrinos. so the calculated abundance could fall into range \[\Omega_pdmh^2=\frac{G^{3/2}T_0^3h^2}{H_0\sigma v}=\frac{3*10-{27} cm^3s^{-1}}{\sigma v}\] research is still on going. Just as the equation of state for the Higgs field may explain inflation as well as the cosmological constant. That should sufficiently show that what really goes on in the professional circles isn't something one can simply google at best that just gives hints

no coordinate choice affects the mass distribution. I could describe the universe in numerous different coordinate choices example Euclidean, spherical cylindrical etc without causing any difference. It is precisely why we use invariance. The mathematics is set up that way so that we do not have any coordinate choice dependency. you know full well GR fully describes time dilation the FLRW metric is a GR solution. We don't arbitrarily choose DM and DE as the full explanation those two terms are simply placeholders until we can determine the cause of each. We still can measure their effects through indirect evidence. I rarely give downvotes so its someone else. As far as sampling range is concerned, redshift is only one of many pieces of evidence of an expanding universe. In point of detail its not even close to the strongest evidence. Its the one most ppl are familiar with but the real evidence comes from our thermodynamic laws in regards to temperature and how it influences the SM model of particles via processes such as BB nucleosynthesis in regards to the CMB. One danger of trying to understand cosmology by rote instead of learning the math is that too often you get incorrect information. I will give an example if I looked up hydrogen and its temperature it could form with stability a google search will state 3000 kelvin. However if one knows how to use the Saha equations that would reveal that value equates to 75 % of the potential hydrogen. Hydrogen can start to form as low as 6000 kelvin=25% 4000 kelvin for 50 %. That is just one example. however knowing this one can study the metallicity of our universe evolution via hydrogen, lithium, deuterium etc. So I just described another piece of evidence for expansion. In other words were not restricted to redshift to determine if our universe is expanding . In point of detail we do not rely on redshift in cosmology it is too full of other influences such as gravitational redshift, transverse redshift, Integrated Sache-Wolfe effect, Doppler redshift. etc etc. We examine all pieces of possible evidence to confirm the accuracy of cosmological redshift. Nor do we use the generic formula everyone sees on google. https://en.wikipedia.org/wiki/Redshift this formula only works for nearby objects it loses accuracy as near as one MPC. The full formula includes the influence of the evolution history of matter, radiation and Lambda. details can be found here "Distance measures in cosmology" David W. Hogg https://arxiv.org/abs/astro-ph/9905116 side note the paper also applies to luminosity distance we also have a different formula for Luminosity distance than what one would google. \[H_O dl=(1+z)|\Omega_k|^{-1/2}sinn[\Omega_k^{1/2} \int^z_o\frac{d\acute{z}}{\sqrt{(1+\acute{z})^2\Omega_R+(1+\acute{z}\Omega_m-\acute{z})(2+\acute{z})\Omega_\Lambda}}]\] What this equation shows is that matter, radiation and Lambda density not only influences expansion rates it also influences redshift and luminosity as well as any curvature term k

No there is no assumptions due to coordinate choice. You already know time dilation is a consequence of spacetime curvature or Relativistic inertia. The math and observational evidence shows us that there is no curvature term k=0. So where would you get time dilation ? This has already previously been mentioned. As massless particles travel at c we can ignore the inertial gamma factor. A higher density past the answer either. To go into greater detail if you take 3 time slices say time now, time at the CMB say z=1100. And a slice at say universe age 7 billion years old. If you describe the geometry of each slice. Each slice has a uniform mass distribution so no slice has a non uniform mass distribution to have a curvature term. Hint this is the real advantage of the scale factor a. No time slice has any change in geometry or curvature it's simply volume change between slices and density changes as a result of the ideal gas laws

Without looking at that link as the material needs to be posted here. The math done in that paper was done by your colleague correct ? By your statement above he refused to describe the mathematics in regards to quantum Strangeness so that paper wouldn't contain that detail with the needed math. Using toroids is nothing new in physics a cyclotron can be described using a toriod geometry. Yes you can mathematically describe any geometry in regards to an earlier comment of yours. Regardless if the person who did the math refused your conjecture then that wouldn't have the math beyond what the two of you were working on.

Add kinematics as it's used in every physics theory including the entirety of the SM model f=ma always applies for example.

Ok let's make it easier for when your looking at Higgs related papers E is energy , \(\rho\) is energy density, v is used for VeV. Think of VeV as a coupling constant for Higgs interactions a lot of the equations apply it in that manner. Energy is the ability to perform work. Energy density is the mean average over some field volume. Three distinct properties with distinctions in the mathematics Hope that helps

Correct the only direct confirmation is via LHC and Atlas etc. Studies are continually improving at each CERN LHC etc upgrade. We barely hit the required energy levels in 2012 so yes research is continually improving.