Mordred

Funny part is the specific QFT equation I'm referring to is very rudimentary. QFT uses normalized units and directly applies the energy momentum equation E^2=P^2+m^2. (In normalized units) For field position you apply the coordinate in x^4 which breaks down to x^0=t, ×^1=x, x^2=y, x^3=z. Nice thing about that is it works well with time derivatives as well. Where the complexity starts to develop is when you add probability for the principle of least action (path taken) and quantum harmonic oscillator. That's where the Euler-Langrangian gets incorporated. Geometry related details gets detailed under the Poincare group. While particle details are under their Lorentz invariant gauge group.

If you apply the Klein Gordon equation you will be Lorentz invariant regardless of geometry changes of spacetime. That is the primary reason why the Klein Gordon equation was developed. The equation directly applies the 4 momentum and four velocity.

Under GR all events are inertial. The geodesic equations include this detail. The Euler Langranian equations are capable of handling wave equations with particle paths. The entire body of QFT incorporate that.

So you believe I for one have never come across a single physics related system or state in neither cosmology or particle physics that I cannot model. So I have never seen the point in attempting to rewrite physics at any stage.

Thanks For pointing that out. I will make the corrections once I get a chance though I may just change that section to a more standardized notation. +1 for catching that appreciate it. edit: Yeah I see what you mean I am going to change it to a more standardized format. Thanks again for the catch. I had pulled it from some old note I had put together a few years back. Likely an older format for the Majorana basis there is better and clearer methods. It was from my older notes when I was studying Majorana. yeah figured out what is the issue is I couldn't recall why I needed the identity matrix [latex]\mathbb{I}[/latex] the format pertains to MSSM where the identity matrix is a requirement. I won't be using this format so will change it to the MSM format with the modern tilde to denote Majorona fields. Its from back when I was studying Majorona under Pati-Salam. Its required for the supersymmetric partner identities. Completely forgot about that lmao

right hand neutrino details to examine in particular 3 LH neutrinos with 4 https://arxiv.org/pdf/1911.05092.pdf https://arxiv.org/pdf/1901.00151.pdf https://arxiv.org/pdf/2109.00767v2.pdf question to examine how many seesaw mechanism would 3 doublet 4 singlet Higgs entail and would this lead to Pati-Salam solutions pertaining to SO(10 MSSM). needs further examination Mikheyev–Smirnov–Wolfenstein (MSW) potential 3.5 KeV xray anomoly https://arxiv.org/abs/1402.2301 requirements sterile neutrino mass terms must be in the KeV range to satisfy sterile neutrinos as a DM candidate

The only thing missing from a GUT is how to keep gravity renormalizable. That may sound easy but merely quantizing spacetime or applying a regulator operator hasn't worked. There are valid SM model theories for DM and DE. What is lacking is the ability to verify the theories. However their are countless viable theories waiting for verification. Inflation is another good example. The Aspic library has tested over 70 viable inflationary models. Narrowing down which ones fit observational data the best via Monte Carlo as well as datasets. One essential step in a successful GUT involves "running of the coupling constants " it is a critical step. Particularly to match thermal equilibrium data. Just because I don't require a new mathematical method and use existing gauge groups via SO(10) does not inhibit my ability to make new findings. If anything it improves my chances by simply looking at each particles thermal equilibrium dropout and projected number density with regards to the expansion history of our universe and trace evidence in the CMB. If I cannot produce accuracy to current datasets then I know something is still missing. I will only be successful if I can match current datasets. Simply claiming to do so isn't sufficient. I must ensure any other person can take my work and reproduce the same results with nothing more than the mathematics and zero verbal explanation. Other than identifying any used variables etc. Hence the necessary mathematical proofs, This simulation for example simply tested our models for accuracy. https://www.illustris-project.org/ So consider this metal exercise take BB at \[10^-43\] seconds. You have a temperature roughly 10^19 Kelvin. the volume is so miniscule that you couldn't have any spacetime curvature aka gravity. How do you have curvature with a volume approximately one Planck length ? How would gravity even make sense ? Literally you can describe that state simply by its temperature and volume everything is in thermal equilibrium so one can apply the Bose-Einstein statistic for photon number density at Blackbody temperature 10^19 Kelvin. You should get roughly 10^90 photons. That is how that calculation comes about that is oft included in Cosmology textbooks. Another interesting detail is neutrinos today. Our universe has a blackbody temperature of 2.7 Kelvin. so ask yourself what the Blackbody of neutrinos are today? Now I can answer that question using nothing more that QM and classical physics ? can your model produce the correct answer? As you have already mentioned the required formula possibly but is that formula an integral aspect of your model or simply employing it to fill the gaps of what your GUT doesn't produce ? I really don't know as I know of 3 different methods to get the correct answer in 3 different theorem. All three are part of the standard model. Now it doesn't really matter if you choose to answer or not. That isn't the point. he point is a good GUT needs to be able to match observational evidence but also be able to match results at ATLAS and other particle accelerators. Given that why would I want any NON standard theory when my very goal is to match data that directly applies Standard theory. aka those Wilson coefficients I mentioned which apply to the QCD range not strictly Higgs. The datasets I need employ them so I need to be able to do so as well

The most commonly method to estimate DM rotation curve due to DM is the NFW profile. It a mass power law method. The essence that it shows is that in order to avoid Kelper curve you must have a uniform distribution of mass surrounding a Galaxy in particular spiral galaxies to offset the bulge. I can't recall the name of the most common DM modelling for early LSS formation beyond it involving Jean's instability.

just setting reminder equations that I find handy, in this case the Langrene that correlates the action of the various particle interations ( close to a unification....lol also reminds me how to do some interesting latex techniques... [latex] \mathcal{L}=\underbrace{\mathbb{R}}_{GR}-\overbrace{\underbrace{\frac{1}{4}F_{\mu\nu}F^{\mu\nu}}_{Yang-Mills}}^{Maxwell}+\underbrace{i\overline{\psi}\gamma^\mu D_\mu \psi}_{Dirac}+\underbrace{|D_\mu h|^2-V(|h|)}_{Higgs}+\underbrace{h\overline{\psi}\psi}_{Yukawa}[/latex] [latex]D_\mu[/latex] minimally coupled gauge covariant derivative. h Higg's bosonic field [latex] \chi[/latex] is the Goldstone boson (not shown above) Goldstone no longer applies after spontaneous symmetry breaking [latex]\overline{\psi}[/latex] is the adjoint spinor [latex]\mathcal{L}_h=|D\mu|^2-\lambda(|h|^2-\frac{v^2}{2})^2[/latex] [latex]D_\mu=\partial_\mu-ie A_\mu[/latex] where [latex] A_\mu[/latex] is the electromagnetic four potential QCD gauge covariant derivative [latex] D_\mu=\partial_\mu \pm ig_s t_a \mathcal{A}^a_\mu[/latex] matrix A represents each scalar gluon field Single Dirac Field [latex]\mathcal{L}=\overline{\psi}I\gamma^\mu\partial_\mu-m)\psi[/latex] under U(1) EM fermion field equates to [latex]\psi\rightarrow\acute{\psi}=e^{I\alpha(x)Q}\psi[/latex] due to invariance requirement of the Langrene above and with the last equation leads to the gauge field [latex]A_\mu[/latex] [latex] \partial_\mu[/latex] is replaced by the covariant derivitave [latex]\partial_\mu\rightarrow D_\mu=\partial_\mu+ieQA_\mu[/latex] where [latex]A_\mu[/latex] transforms as [latex]A_\mu+\frac{1}{e}\partial_\mu\alpha[/latex] Single Gauge field U(1) [latex]\mathcal{L}=\frac{1}{4}F_{\mu\nu}F^{\mu\nu}[/latex] [latex]F_{\mu\nu}=\partial_\nu A_\mu-\partial_\mu A_\nu[/latex] add mass which violates local gauge invariance above [latex]\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\frac{1}{2}m^2A_\mu A^\mu[/latex] guage invariance demands photon be massless to repair gauge invariance add a single complex scalar field [latex]\phi=\frac{1}{\sqrt{2}}(\phi_1+i\phi_2[/latex] Langrene becomes [latex] \mathcal{L}=\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+|D_\mu \phi|^2-V_\phi[/latex] where [latex]D_\mu=\partial_\mu-ieA_\mu[/latex] [latex]V_\phi=\mu^2|\phi^2|+\lambda(|\phi^2|)^2[/latex] [latex]\overline{\psi}=\psi^\dagger \gamma^0[/latex] where [latex]\psi^\dagger[/latex] is the hermitean adjoint and [latex]\gamma^0 [/latex] is the timelike gamma matrix the four contravariant matrix are as follows [latex]\gamma^0=\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}[/latex] [latex]\gamma^1=\begin{pmatrix}0&0&0&1\\0&0&1&0\\0&0&-1&0\\-1&0&0&0\end{pmatrix}[/latex] [latex]\gamma^2=\begin{pmatrix}0&0&0&-i\\0&0&i&0\\0&i&0&0\\-i&0&0&0\end{pmatrix}[/latex] [latex]\gamma^3=\begin{pmatrix}0&0&1&0\\0&0&0&-1\\-1&0&0&0\\0&1&0&0\end{pmatrix}[/latex] where [latex] \gamma^0[/latex] is timelike rest are spacelike V denotes the CKM matrix usage [latex]\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}[/latex] [latex]V_{ckm}=V^\dagger_{\mu L} V_{dL}[/latex] the CKM mixing angles correlates the cross section between the mass eigenstates and the weak interaction eigenstates. Involves CP violations and chirality relations. Dirac 4 component spinor fields [latex]\gamma^5=i\gamma_0,\gamma_1,\gamma_2,\gamma_3[/latex] 4 component Minkowskii with above 4 component Dirac Spinor and 4 component Dirac gamma matrixes are defined as [latex] {\gamma^\mu\gamma^\nu}=2g^{\mu\nu}\mathbb{I}[/latex] where [latex]\mathbb{I}[/latex] is the identity matrix. (required under MSSM electroweak symmetry break} in Chiral basis [latex]\gamma^5[/latex] is diagonal in [latex]2\otimes 2[/latex] the gamma matrixes are [latex]\begin{pmatrix}0&\sigma^\mu_{\alpha\beta}\\\overline{\sigma^{\mu\dot{\alpha}\beta}}&0\end{pmatrix}[/latex] [latex]\gamma^5=i{\gamma_0,\gamma_1,\gamma_2,\gamma_3}=\begin{pmatrix}-\delta_\alpha^\beta&0\\0&\delta^\dot{\alpha}_\dot{\beta}\end{pmatrix}[/latex] [latex]\mathbb{I}=\begin{pmatrix}\delta_\alpha^\beta&0\\0&\delta^\dot{\alpha}_\dot{\beta}\end{pmatrix}[/latex] Lorentz group identifiers in [latex](\frac{1}{2},0)\otimes(0,\frac{1}{2})[/latex] [latex]\sigma\frac{I}{4}=(\gamma^\mu\gamma^\nu)=\begin{pmatrix}\sigma^{\mu\nu\beta}_{\alpha}&0\\0&-\sigma^{\mu\nu\dot{\alpha}}_{\dot{\beta}}\end{pmatrix}[/latex] [latex]\sigma^{\mu\nu}[/latex] duality satisfies [latex]\gamma_5\sigma^{\mu\nu}=\frac{1}{2}I\epsilon^{\mu\nu\rho\tau}\sigma_{\rho\tau}[/latex] a 4 component Spinor Dirac field is made up of two mass degenerate Dirac spinor fields U(1) helicity [latex](\chi_\alpha(x)),(\eta_\beta(x))[/latex] [latex]\psi(x)=\begin{pmatrix}\chi^{\alpha\beta}(x)\\ \eta^{\dagger \dot{\alpha}}(x)\end{pmatrix}[/latex] the [latex](\alpha\beta)=(\frac{1}{2},0)[/latex] while the [latex](\dot{\alpha}\dot{\beta})=(0,\frac{1}{2})[/latex] this section relates the SO(4) double cover of the SU(2) gauge requiring the chiral projection operator next. chiral projections operator [latex]P_L=\frac{1}{2}(\mathbb{I}-\gamma_5=\begin{pmatrix}\delta_\alpha^\beta&0\\0&0\end{pmatrix}[/latex] [latex]P_R=\frac{1}{2}(\mathbb{I}+\gamma_5=\begin{pmatrix}0&0\\ 0&\delta^\dot{\alpha}_\dot{\beta}\end{pmatrix}[/latex] Weyl spinors [latex]\psi_L(x)=P_L\psi(x)=\begin{pmatrix}\chi_\alpha(x)\\0\end{pmatrix}[/latex] [latex]\psi_R(x)=P_R\psi(x)=\begin{pmatrix}0\\ \eta^{\dagger\dot{a}}(x)\end{pmatrix}[/latex] also requires Yukawa couplings...SU(2) matrixes given by [latex]diag(Y_{u1},Y_{u2},Y_{u3})=diag(Y_u,Y_c,Y_t)=diag(L^t_u,\mathbb{Y}_u,R_u)[/latex] [latex]diag(Y_{d1},Y_{d2},Y_{d3})=diag(Y_d,Y_s,Y_b)=diag(L^t_d,\mathbb{Y}_d,R_d[/latex] [latex]diag(Y_{\ell 1},Y_{\ell 2},Y_{\ell3})=diag(Y_e,Y_\mu,Y_\tau)=diag(L^T_\ell,\mathbb{Y}_\ell,R_\ell)[/latex] the fermion masses [latex]Y_{ui}=m_{ui}/V_u[/latex] [latex]Y_{di}=m_{di}/V_d[/latex] [latex]Y_{\ell i}=m_{\ell i}/V_\ell[/latex] Reminder notes: Dirac is massive 1/2 fermions, Weyl the massless. Majorona fermion has its own antiparticle pair while Dirac and Weyl do not. The RH neutrino would be more massive than the LH neutrino, same for the corresponding LH antineutrino and RH Neutrino via seesaw mechanism which is used with the seesaw mechanism under MSM. Under MSSM with different Higgs/higglets can be numerous seesaws. The Majorona method has conservation violations also these fermions must be electric charge neutral. (must be antiparticles of themselves) the CKM and PMNS are different mixing angels in distinction from on another. However they operate much the same way. CKM is more commonly used as its better tested to higher precision levels atm. Quark family is Dirac fermions due to electric charge cannot be its own antiparticle. Same applies to the charged lepton family. Neutrinos are members of the charge neutral lepton family CKM is also a different parametrisation than the Wolfenstein Parametrization in what way (next study) Lorentz group Lorentz transformations list spherical coordinates (rotation along the z axis through an angle ) \[\theta\] \[(x^0,x^1,x^2,x^3)=(ct,r,\theta\phi)\] \[(x_0,x_1,x_2,x_3)=(-ct,r,r^2,\theta,[r^2\sin^2\theta]\phi)\] \[\acute{x}=x\cos\theta+y\sin\theta,,,\acute{y}=-x\sin\theta+y \cos\theta\] \[\Lambda^\mu_\nu=\begin{pmatrix}1&0&0&0\\0&\cos\theta&\sin\theta&0\\0&\sin\theta&\cos\theta&0\\0&0&0&1\end{pmatrix}\] generator along z axis \[k_z=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}\] generator of boost along x axis:: \[k_x=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}=-i\begin{pmatrix}0&1&0&0\\1&0&0&0\\0&0&0&0\\0&0&0&0 \end{pmatrix}\] boost along y axis\ \[k_y=-i\begin{pmatrix}0&0&1&0\\0&0&0&0\\1&0&0&0\\0&0&0&0 \end{pmatrix}\] generator of boost along z direction \[k_z=-i\begin{pmatrix}0&0&0&1\\0&0&0&0\\0&0&0&0\\1&0&0&0 \end{pmatrix}\] the above is the generator of boosts below is the generator of rotations. \[J_z=\frac{1\partial\Lambda}{i\partial\theta}|_{\theta=0}\] \[J_x=-i\begin{pmatrix}0&0&0&0\\0&0&0&0\\0&0&0&1\\0&0&-1&0 \end{pmatrix}\] \[J_y=-i\begin{pmatrix}0&0&0&0\\0&0&0&-1\\0&0&1&0\\0&0&0&0 \end{pmatrix}\] \[J_z=-i\begin{pmatrix}0&0&0&0\\0&0&1&0\\0&-1&0&0\\0&0&0&0 \end{pmatrix}\] there is the boosts and rotations we will need and they obey commutations \[[A,B]=AB-BA\] SO(3) Rotations list set x,y,z rotation as \[\varphi,\Phi\phi\] \[R_x(\varphi)=\begin{pmatrix}1&0&0\\0&\cos\varphi&\sin\varphi\\o&-sin\varphi&cos\varphi \end{pmatrix}\] \[R_y(\phi)=\begin{pmatrix}cos\Phi&0&\sin\Phi\\0&1&0\\-sin\Phi&0&cos\Phi\end{pmatrix}\] \[R_z(\phi)=\begin{pmatrix}cos\theta&sin\theta&0\\-sin\theta&\cos\theta&o\\o&0&1 \end{pmatrix}\] Generators for each non commutative group. \[J_x=-i\frac{dR_x}{d\varphi}|_{\varphi=0}=\begin{pmatrix}0&0&0\\0&0&-i\\o&i&0\end{pmatrix}\] \[J_y=-i\frac{dR_y}{d\Phi}|_{\Phi=0}=\begin{pmatrix}0&0&-i\\0&0&0\\i&i&0\end{pmatrix}\] \[J_z=-i\frac{dR_z}{d\phi}|_{\phi=0}=\begin{pmatrix}0&-i&0\\i&0&0\\0&0&0\end{pmatrix}\] with angular momentum operator \[{J_i,J_J}=i\epsilon_{ijk}J_k\] with Levi-Civita \[\varepsilon_{123}=\varepsilon_{312}=\varepsilon_{231}=+1\] \[\varepsilon_{123}=\varepsilon_{321}=\varepsilon_{213}=-1\] SU(3) generators Gell Mann matrix's \[\lambda_1=\begin{pmatrix}0&-1&0\\1&0&0\\0&0&0\end{pmatrix}\] \[\lambda_2=\begin{pmatrix}0&-i&0\\i&0&0\\0&0&0\end{pmatrix}\] \[\lambda_3=\begin{pmatrix}1&0&0\\0&-1&0\\0&0&0\end{pmatrix}\] \[\lambda_4=\begin{pmatrix}0&0&1\\0&0&0\\1&0&0\end{pmatrix}\] \[\lambda_5=\begin{pmatrix}0&0&-i\\0&0&0\\i&0&0\end{pmatrix}\] \[\lambda_6=\begin{pmatrix}0&0&0\\0&0&1\\0&1&0\end{pmatrix}\] \[\lambda_7=\begin{pmatrix}0&0&0\\0&0&-i\\0&i&0\end{pmatrix}\] \[\lambda_8=\frac{1}{\sqrt{3}}\begin{pmatrix}1&0&0\\0&1&0\\0&0&-2\end{pmatrix}\] commutation relations \[[\lambda_i\lambda_j]=2i\sum^8_{k=1}f_{ijk}\lambda_k\] with algebraic structure \[f_{123}=1,f_{147}=f_{165}=f_{246}=f_{246}=f_{257}=f_{345}=f_{376}=\frac{1}{2},f_{458}=f_{678}=\frac{3}{2}\] with Casimer Operator \[\vec{J}^2=J_x^2+J_y^2+j_z^2\]

Some of the aspects, I came across by doing the calculations and I will use Hydrogen thermal equilibrium dropout as an example. If one employs the Saha equations instead of relying on literature. One discovers that the hydrogen dropout value of 3000 kelvin only represents the value at the 75% mark. Hydrogen will begin drop out previous to that. At 6000 kelvin the % is 25%, at 4500 Kelvin the percentage is at 50%. It is details such as this that become apparent when one looks beyond literature, performs his own calculations and doesn't rely on merely verbal descriptions. Another example is that by applying the Langrangian creation and annihilation operators one can get a more exacting value for number density (albiet its a probability density) that applying Maxwell Boltzmann. Which is the more common methodology. Both are equally valid, but each method has its pros and cons. Maxwell Boltzmann is a far easier method but is more an first order approximation comparatively. Where as the former method makes it far easier to cross check with collider datasets for key aspects and works well with Feymann integrals

Trust me there will be very little comparison between your model and ideas and mine lol. Everything in my models use the standardized physics methodologies. I didn't have to create a single formula beyond deriving the elements I require out of them from the mathematical proofs of the existing formulas. These threads I have been using as a sort of whiteboard with regards to some of the formulas I am deploying. https://www.scienceforums.net/topic/128332-early-universe-nucleosynthesis/ Orion and I spent some time breaking apart the Covariant derivative form of the SM Langrangian mainly to cross check its validity while Orion worked on the relativity portion. wish he was still around as he excelled at applying Maxwell Boltzmann applications. one of the tools I will be using for cross check accuracy is \[{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&T (Gy)&R (Gly)&D_{now} (Gly)&Temp(K) \\ \hline 2.00e+4&1.86e-6&3.49e-6&4.62e+1&5.45e+4\\ \hline 1.73e+4&2.45e-6&4.62e-6&4.62e+1&4.71e+4\\ \hline 1.49e+4&3.23e-6&6.10e-6&4.62e+1&4.07e+4\\ \hline 1.29e+4&4.25e-6&8.04e-6&4.61e+1&3.52e+4\\ \hline 1.12e+4&5.60e-6&1.06e-5&4.61e+1&3.04e+4\\ \hline 9.66e+3&7.37e-6&1.39e-5&4.61e+1&2.63e+4\\ \hline 8.35e+3&9.70e-6&1.83e-5&4.61e+1&2.27e+4\\ \hline 7.21e+3&1.28e-5&2.39e-5&4.61e+1&1.97e+4\\ \hline 6.24e+3&1.68e-5&3.12e-5&4.60e+1&1.70e+4\\ \hline 5.39e+3&2.20e-5&4.07e-5&4.60e+1&1.47e+4\\ \hline 4.66e+3&2.87e-5&5.29e-5&4.60e+1&1.27e+4\\ \hline 4.03e+3&3.75e-5&6.85e-5&4.59e+1&1.10e+4\\ \hline 3.48e+3&4.89e-5&8.86e-5&4.59e+1&9.49e+3\\ \hline 3.01e+3&6.36e-5&1.14e-4&4.58e+1&8.21e+3\\ \hline 2.60e+3&8.25e-5&1.47e-4&4.58e+1&7.09e+3\\ \hline 2.25e+3&1.07e-4&1.88e-4&4.57e+1&6.13e+3\\ \hline 1.94e+3&1.38e-4&2.41e-4&4.57e+1&5.30e+3\\ \hline 1.68e+3&1.78e-4&3.08e-4&4.56e+1&4.58e+3\\ \hline 1.45e+3&2.28e-4&3.92e-4&4.55e+1&3.96e+3\\ \hline 1.26e+3&2.93e-4&4.98e-4&4.54e+1&3.42e+3\\ \hline 1.09e+3&3.75e-4&6.31e-4&4.53e+1&2.96e+3\\ \hline 9.38e+2&4.78e-4&7.98e-4&4.52e+1&2.56e+3\\ \hline 8.11e+2&6.09e-4&1.01e-3&4.51e+1&2.21e+3\\ \hline 7.01e+2&7.74e-4&1.27e-3&4.50e+1&1.91e+3\\ \hline 6.06e+2&9.83e-4&1.60e-3&4.49e+1&1.65e+3\\ \hline 5.24e+2&1.24e-3&2.01e-3&4.47e+1&1.43e+3\\ \hline 4.52e+2&1.57e-3&2.53e-3&4.46e+1&1.24e+3\\ \hline 3.91e+2&1.99e-3&3.17e-3&4.44e+1&1.07e+3\\ \hline 3.38e+2&2.50e-3&3.97e-3&4.42e+1&9.23e+2\\ \hline 2.92e+2&3.15e-3&4.97e-3&4.40e+1&7.98e+2\\ \hline 2.52e+2&3.96e-3&6.22e-3&4.38e+1&6.90e+2\\ \hline 2.18e+2&4.98e-3&7.77e-3&4.35e+1&5.97e+2\\ \hline 1.88e+2&6.25e-3&9.71e-3&4.33e+1&5.16e+2\\ \hline 1.63e+2&7.83e-3&1.21e-2&4.30e+1&4.46e+2\\ \hline 1.40e+2&9.81e-3&1.51e-2&4.27e+1&3.85e+2\\ \hline 1.21e+2&1.23e-2&1.89e-2&4.24e+1&3.33e+2\\ \hline 1.05e+2&1.53e-2&2.35e-2&4.20e+1&2.88e+2\\ \hline 9.04e+1&1.92e-2&2.94e-2&4.16e+1&2.49e+2\\ \hline 7.80e+1&2.40e-2&3.66e-2&4.12e+1&2.15e+2\\ \hline 6.73e+1&2.99e-2&4.56e-2&4.08e+1&1.86e+2\\ \hline 5.80e+1&3.74e-2&5.68e-2&4.03e+1&1.61e+2\\ \hline 5.00e+1&4.66e-2&7.07e-2&3.98e+1&1.39e+2\\ \hline 4.31e+1&5.81e-2&8.81e-2&3.93e+1&1.20e+2\\ \hline 3.71e+1&7.25e-2&1.10e-1&3.87e+1&1.04e+2\\ \hline 3.20e+1&9.03e-2&1.37e-1&3.81e+1&8.98e+1\\ \hline 2.75e+1&1.13e-1&1.70e-1&3.74e+1&7.76e+1\\ \hline 2.36e+1&1.40e-1&2.12e-1&3.66e+1&6.71e+1\\ \hline 2.03e+1&1.75e-1&2.63e-1&3.59e+1&5.80e+1\\ \hline 1.74e+1&2.18e-1&3.28e-1&3.50e+1&5.02e+1\\ \hline 1.49e+1&2.71e-1&4.08e-1&3.41e+1&4.34e+1\\ \hline 1.28e+1&3.37e-1&5.08e-1&3.31e+1&3.75e+1\\ \hline 1.09e+1&4.20e-1&6.32e-1&3.21e+1&3.24e+1\\ \hline 9.28e+0&5.23e-1&7.86e-1&3.09e+1&2.80e+1\\ \hline 7.89e+0&6.51e-1&9.78e-1&2.97e+1&2.42e+1\\ \hline 6.68e+0&8.10e-1&1.22e+0&2.84e+1&2.09e+1\\ \hline 5.64e+0&1.01e+0&1.51e+0&2.70e+1&1.81e+1\\ \hline 4.74e+0&1.25e+0&1.88e+0&2.55e+1&1.56e+1\\ \hline 3.96e+0&1.56e+0&2.33e+0&2.38e+1&1.35e+1\\ \hline 3.29e+0&1.94e+0&2.88e+0&2.21e+1&1.17e+1\\ \hline 2.71e+0&2.40e+0&3.56e+0&2.02e+1&1.01e+1\\ \hline 2.21e+0&2.98e+0&4.38e+0&1.83e+1&8.74e+0\\ \hline 1.77e+0&3.69e+0&5.35e+0&1.62e+1&7.55e+0\\ \hline 1.40e+0&4.55e+0&6.49e+0&1.39e+1&6.53e+0\\ \hline 1.07e+0&5.58e+0&7.79e+0&1.16e+1&5.64e+0\\ \hline 7.91e-1&6.82e+0&9.19e+0&9.25e+0&4.88e+0\\ \hline 5.48e-1&8.27e+0&1.07e+1&6.85e+0&4.22e+0\\ \hline 3.38e-1&9.92e+0&1.21e+1&4.47e+0&3.65e+0\\ \hline 1.57e-1&1.18e+1&1.34e+1&2.16e+0&3.15e+0\\ \hline 0.00e+0&1.38e+1&1.44e+1&0.00e+0&2.73e+0\\ \hline -1.36e-1&1.60e+1&1.53e+1&2.03e+0&2.36e+0\\ \hline -2.48e-1&1.81e+1&1.59e+1&3.79e+0&2.05e+0\\ \hline -3.46e-1&2.04e+1&1.64e+1&5.37e+0&1.78e+0\\ \hline -4.31e-1&2.27e+1&1.67e+1&6.77e+0&1.55e+0\\ \hline -5.05e-1&2.50e+1&1.69e+1&8.02e+0&1.35e+0\\ \hline -5.69e-1&2.74e+1&1.71e+1&9.11e+0&1.17e+0\\ \hline -6.25e-1&2.98e+1&1.72e+1&1.01e+1&1.02e+0\\ \hline -6.74e-1&3.22e+1&1.72e+1&1.09e+1&8.88e-1\\ \hline -7.16e-1&3.46e+1&1.73e+1&1.16e+1&7.73e-1\\ \hline -7.53e-1&3.70e+1&1.73e+1&1.23e+1&6.72e-1\\ \hline -7.85e-1&3.94e+1&1.73e+1&1.28e+1&5.85e-1\\ \hline -8.13e-1&4.18e+1&1.73e+1&1.33e+1&5.09e-1\\ \hline -8.38e-1&4.43e+1&1.74e+1&1.37e+1&4.42e-1\\ \hline -8.59e-1&4.67e+1&1.74e+1&1.41e+1&3.85e-1\\ \hline -8.77e-1&4.91e+1&1.74e+1&1.44e+1&3.35e-1\\ \hline -8.93e-1&5.15e+1&1.74e+1&1.47e+1&2.91e-1\\ \hline -9.07e-1&5.39e+1&1.74e+1&1.49e+1&2.53e-1\\ \hline -9.19e-1&5.64e+1&1.74e+1&1.52e+1&2.20e-1\\ \hline -9.30e-1&5.88e+1&1.74e+1&1.53e+1&1.92e-1\\ \hline -9.39e-1&6.12e+1&1.74e+1&1.55e+1&1.67e-1\\ \hline -9.47e-1&6.36e+1&1.74e+1&1.56e+1&1.45e-1\\ \hline -9.54e-1&6.60e+1&1.74e+1&1.58e+1&1.26e-1\\ \hline -9.60e-1&6.85e+1&1.74e+1&1.59e+1&1.10e-1\\ \hline -9.65e-1&7.09e+1&1.74e+1&1.60e+1&9.55e-2\\ \hline -9.70e-1&7.33e+1&1.74e+1&1.60e+1&8.31e-2\\ \hline -9.73e-1&7.57e+1&1.74e+1&1.61e+1&7.23e-2\\ \hline -9.77e-1&7.81e+1&1.74e+1&1.62e+1&6.29e-2\\ \hline -9.80e-1&8.06e+1&1.74e+1&1.62e+1&5.47e-2\\ \hline -9.83e-1&8.30e+1&1.74e+1&1.63e+1&4.76e-2\\ \hline -9.85e-1&8.54e+1&1.74e+1&1.63e+1&4.14e-2\\ \hline -9.87e-1&8.78e+1&1.74e+1&1.63e+1&3.60e-2\\ \hline -9.89e-1&9.02e+1&1.74e+1&1.64e+1&3.13e-2\\ \hline -9.90e-1&9.27e+1&1.74e+1&1.64e+1&2.73e-2\\ \hline \end{array}}\] Jorrie and Cuthberd must be adding features I will have to contact them its not allowing the full column selection range at least not with the latex options. It does for the standard format. Likely they are working on the glitch already but will check p and make sure they are aware of it. \[{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&Scale (a)&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&H(t)&Temp(K) \\ \hline 1.09e+3&9.17e-4&3.72e-4&6.27e-4&4.53e+1&4.16e-2&5.67e-2&8.52e-4&1.55e+6&2.97e+3\\ \hline 3.39e+2&2.94e-3&2.49e-3&3.95e-3&4.42e+1&1.30e-1&1.79e-1&6.11e-3&2.46e+5&9.27e+2\\ \hline 1.05e+2&9.44e-3&1.53e-2&2.34e-2&4.20e+1&3.97e-1&5.53e-1&4.01e-2&4.15e+4&2.89e+2\\ \hline 3.20e+1&3.03e-2&9.01e-2&1.36e-1&3.81e+1&1.15e+0&1.65e+0&2.48e-1&7.15e+3&9.00e+1\\ \hline 9.29e+0&9.71e-2&5.22e-1&7.84e-1&3.09e+1&3.00e+0&4.61e+0&1.49e+0&1.24e+3&2.81e+1\\ \hline 2.21e+0&3.12e-1&2.98e+0&4.37e+0&1.83e+1&5.69e+0&1.09e+1&8.73e+0&2.23e+2&8.74e+0\\ \hline 0.00e+0&1.00e+0&1.38e+1&1.44e+1&0.00e+0&0.00e+0&1.65e+1&4.63e+1&6.74e+1&2.73e+0\\ \hline -6.88e-1&3.21e+0&3.30e+1&1.73e+1&1.12e+1&3.58e+1&1.73e+1&1.84e+2&5.64e+1&8.49e-1\\ \hline -8.68e-1&7.58e+0&4.79e+1&1.74e+1&1.43e+1&1.08e+2&1.74e+1&4.59e+2&5.61e+1&3.59e-1\\ \hline -9.44e-1&1.79e+1&6.28e+1&1.74e+1&1.56e+1&2.79e+2&1.74e+1&1.11e+3&5.60e+1&1.52e-1\\ \hline -9.76e-1&4.23e+1&7.77e+1&1.74e+1&1.61e+1&6.84e+2&1.74e+1&2.64e+3&5.60e+1&6.44e-2\\ \hline -9.90e-1&1.00e+2&9.27e+1&1.74e+1&1.64e+1&1.64e+3&1.74e+1&6.27e+3&5.60e+1&2.73e-2\\ \hline \end{array}}\] Anyways The above calculator which Myself, Jorrie, Cuthberd and Markus were involved in the development though in my case it was mainly error checking and writing up some of the guides to how to use it while Jorrie and Cuthberd handled the programming aspects. Markus mainly did his best on advertising and aiding others in using it as well as crosschecks. Unfortunately he passed away a few years back. Its is a handy tool as one can apply any dataset to it and it greatly saves on calculations using the primary formulas of the FLRW metric. The nucleosynthesis thread has the major formulas I will be employing along with the SM Langrange. I am currently working on the family generations aspects. Already have the required math just need to cross check a few details. Needless to say I'm not developing a GUT I am applying SO(10) MSM, the FLRW metric, QFT and GR. The calculator uses the methodology by Lineweaver and Davies in particular stretch, (inverse of scale factor, which coincidentally also gives temperature. Much of the methodology I will be using is covered in the following articles http://www.wiese.itp.unibe.ch/lectures/universe.pdf http://arxiv.org/pdf/hep-th/0503203.pdf in essence I am simply attempting more exacting solutions with more modern datasets and methodologies,

Very accurate assessment love the analogy. At the same time I'm getting a handle on the methods Baron used instead of being forced to cut and paste pages and pages of details from the work he has already done.

Specific timings, number densities of the SM particle thermal equilibrium dropout stages and subsequently BB nucleosynthesis for metalicity percentages of hydrogen, deuterium, lithium. In essence updating the actual values of each stage. From 10^-43 seconds to surface of last scattering up to z=1100. Ok that helps clarify a few details. The Higgs related details I'm waiting for is directly related to finer precision on mass values which directly correlate to thermal equilibrium dropout values

I am curious if you've ever considered Wilson loops coefficients ? I honestly believe it would be a useful addition. Particularly as it also involves Landau coefficients as well as Rheimann zeta functions. Here is an example paper https://arxiv.org/abs/1809.06787 The primary advantage is that the LHC and Atlas datasets also employ them for their channels with regards to relevant Breit Wigner cross sections ie the cross sections above for Higgs I gave are in Breit Wigner form.

Thought that might interest you. As an avid reader of numerous models over the years If I have learned anything it's that any applicable mathematical method can be used. One can often find literature showing its already been attempted or applied. The methodology I typically use for second order phase transition of Higgs I typically approach it utilizing QFT as it is a second order model. Quantum effects in first order one can use QM. With Higgs the research aspects I'm waiting directly involve the Higgs cross sections. Higgs cross sections \[\Gamma(H\rightarrow f\bar{f})=\frac{G_Fm_f^2m_HN_c}{4\pi \sqrt{2}}(1-4m^2_f/m^2_H)^{3/2}\] \[\Gamma(H\rightarrow W^+ W^-)=\frac{GF M^3_H\beta_W}{32\pi\sqrt{2}}(4-4a_w+3a_W^2)\] \[\Gamma(H\rightarrow ZZ)=\frac{GF M^3_H\beta_z}{64\pi\sqrt{2}}(4-4a_Z+3a_Z^2)\] with the CKMS matrix and the relevant Weinberg angles. Which will directly relate to mass term precision.

If your applying Landeau coefficients with regards to Higgs metastability with phase transitions involving electroweak symmetry breaking this brief article might interest you. https://arxiv.org/pdf/1911.08893 If so his references will likely lead to other related studies in this methodology

There is nothing wrong with different approaches to any physics model. Every approach can and often does reveal details previous approaches do not. You might note I never once stated your theory crazy or wildly imaginative.. I simply wanted to see if you had the ability to accurately model your ideas. This is the primary reason I come to forums. To help others learn. I'm knowledgeable enough in physics to research any questions on a specific model on my own without any help or aid. Just as I can accurately generate my own models of any physics related process. Though 95 percent of the time I can prove new models I generate in error or insufficient to to add to the physics community. I have a few models on Higgs in cosmology applications I'm still working on and awaiting for better research in the metastability regime. Though I would recommend only claim what you can mathematically show via a mathematical proof when requested. Far too often posters and even professional physicist state their model can solve such and such, but then papers don't include the relevant solutions with the mathematics. DE and DM claims are very common yet most times they can only provide mainstream related formulas to those two entities and simply show compatibility to model what is already known about them

Well I'm glad your not attempting that claim. Considering back when I was an undergrad my primary interest was processes that could lead to particle production both virtual and real. I literally lost count of the number of variations I've read over the years. Lol for that matter the creation/annihilation operators of QFT are well designed to predict the probable number density of states given any field energy level for any particle via the relevant wave equations included in the formula for either bosons or fermions. There is nothing new about the idea. It's literally part and parcel with mainstream physics. Edit most ppl nowadays don't even remember that Parker radiation involved particle production from the curvature terms of spacetime. Nowadays it's used in MRIs and x Ray machines.

I sincerely hope your not trying to claim the process mentioned in that paper as your own idea and claim they stole it from you. The idea that gravity waves can affect the EM field to generate photons as a result has literally been around for decades. Nearly as long as gravity waves were initially proposed. I've read numerous papers a couple of decades ago that described the very same process. Copeland however had an inflationary model built describing a very similar process published in the late 60's

The truth is no matter how good a mathematical proof may be Observational evidence can easily Trump it. A math proof shows feasibility. Without seeing your entire model it's impossible to tell whether it can perform everything you claim. Including DE and DM. I'm also unclear how your handling vectors and Spinor relations which are particularly important with regards to numerous aspects of a particle. I do know the Rheimann zeta function can be used but I have only read a few articles applying it to spin statistics where the majority of the articles didn't cover the Dirac field for fermionic spins. Don't be offended if I stick with the mainstream physics after 35 years studying and applying it. It's never failed me for any of the work I do.

Furthe question to clarify your application involving the Rheimann zeta function I assume you include the Mandelstrom variables?

Thank you for clarifying how you are deploying your dimensions and subsequently your indices. A large part of all the edits is getting my equations into latex format. You have to save often. Working with pmatrix structures can get annoying. Had you included this at the beginning it would have greatly helped avoid much of the previous posts. This was the kind of detail I was looking for. I noticed you didn't include the Dirac field for spin half particles. So how are you handling particle spin for the fermionic fields ?

Well if it helps The various probabilities for number density of a particle will rely on phase space which can be understood as the particle in a box images and videos. The mathematical methodology of both employ the particle states wavefunctions. this also will better help with regards to spin statistics.

your obviously not using Einstein index notation. You really need to properly define your dimensions. What does each dimension specifically represent ? That likely is the confusion https://en.wikipedia.org/wiki/Einstein_notation especially if your referring to it as an 11 dimensional METRIC Tensor. see range of values for ij by convention in the link provided. This is an issue if one wishes to perform vector calculus from your tensors. explain as standard spacetime coordinates is (t,x,y,z) which is only 4 dimensions what are the additional dimensions and why would you require them when applying the action principle which describes particle paths via the principle of least action of the Euler_Langrangian. Look at the specifics with regards to the 4 momentum of GR. What you seem to be implying is some personal 11 vector I have no idea what you would call that but I cannot see how you can state it describes potential and or kinetic energy relations via the action principle. lets try an example apply Newtonian force provided by the following equation \[F^i=dp^i/d\tau\] where in standard usage and lets use spherical coordinates \[g_{ij}=\begin{pmatrix}1&0&0\\0&r^2&0\\0&1&r^2sin^2\theta\end{pmatrix}\] \[g^{ij}=\begin{pmatrix}1&0&0\\0&r^{-2}&0\\0&1&r^{-2}sin^{-2}\theta\end{pmatrix}\] in Euclidean coordinates which is the standard usage for \[g_{ij}\] explain your coordinate system if does not follow this as this is the standardized usage in any calculus textbookn which further correlates to the Cauchy stress tensor. This is also what the Kronecker Delta applies to. curved spacetime has additional transformations and as such requires the Levi Civita connections. https://en.wikipedia.org/wiki/Cauchy_stress_tensor Note none of this post involves spacetime but simply kinematics in Euclidean space which preserves Pythagoras theorem for any relevent trigonometric operations obviously spacetime requires additional transformation laws to do the same. How do you preserve those same laws in your 11 dimensional space ? How do you apply vector notation with the applicable covector/contravector terms ? How do you preserve Lorentz invariant which requires a vector and covector (google one forms for further detail) note for the above the i/j=set of {1,2,3} your models seems to require the set of 1 to 11 for i/j. Provided by you with D^11 as you describe as your metric tensor If you claim your model works with this as being the correct then how can you possibly claim the inverse of an 11 dimensional tensor is the equivalent of a 3 dimensional tensor given by standardized Calculus ? Particularly since you have not provided any transformation laws regarding your geometry to allow a transformation to the Euclidean metric. An example of such transformation laws being the Lorentz transforms https://en.wikipedia.org/wiki/Lorentz_transformation note the inverse of a 4 by 4 matrix is another 4 by 4 matrix so its inverse is also not g_{ij] this is given by notation\[AA^{-1}=1\] any square matrix is invertible provided the resultant is not singular \[AA^{-1}=0\] for a singular matrix definition, I will assume you know one of its uses of inverting a matrix is that one cannot divide a matrix so one must multiply by its inverse. So this is a divide by zero error hence the namesake.

That's a fairly accurate description it would act very similar to merging galaxies albeit on a smaller scale. Other difference would also involve a difference in percentages in charged ion behavior in regards to the relevant Poynting vectors and Compton scattering . Relevant luminosity of course involving the peak wavelengths.