Mordred

Well first off atoms didn't exist yet they come later. The particles of the SM were in a state called thermal equilibrium. I'm essence they are so energetic and short lived that individual particles cannot be distinguished from one another (similar to a Bose Einstein condensate state). You can't think of mass being some weight or matter object mass is resistance to inertia change. It is a property objects, states, fields have not a thing unto itself

As mentioned the BB model starts at a hot dense state from 10^{-43) forward. It does not describe what caused the BB itself. Infinitesimal crop into the mathematics before the time above. The FLRW metric is valid for the entire expansion history. The FLRW metric is well supported by the observational evidence. Starting from a BH isn't part of the model thar is simply one of the many alternative models to describe how it started.

lol that's the one accidently replied in the other thread. The T=1490 with T=4000 is 50% decoupling. Hence the recombination Epoch where the mean free path of photons becomes near infinite is set at the T=3000 K Z-1100. age 366,000 T=6000 can be representative of the early stages of decoupling at Z=2189 giving age at 112,000 years calculation based on 2018 dataset

That's the one, I have a luminosity distance to z relation I wanted to verify however may also look at determining age of stars.

Interesting in the following article it describes the reaction rate of Hydrogen as it drops out of thermal equilibrium. Using the temperature to redshift relation T=T0(1+z) or alternateIy the inverse of the scale factor a. I calculated the temperature of 4000 kelvin to z= 1492. The article evidently rounded this to z=5000, this corresponds to universe age 218,000 years old for the universe. The table also shows the reaction rate for higher and lower temperature values. https://iopscience.iop.org/article/10.3847/1538-4357/ab2d2f/pdf. This additionally tested the mathematics I was examining using a method by Juan Garcıa-Bellido. Details are in the following thread. For the Nucleosynthesis calculation to get an accurate method to correlate redshift to temperature relations so as I examine when different particle species drop out of thermal equilibrium I can calculate the age of the universe, volume, and subsequently the number density of each particle species. You often see in literature the value of 3000 kelvin given. Results are in the above article, using the method of said article. This corresponds to Z=1100 roughly 350,000 Years age for the Observable universe. The conjecture I am going to examine next is that at Higher temperature in the chart of said article the photon interactions with hydrogen atoms will cause higher scatterings of the atoms. Hence the 3000 Kelvin value is the more stable decoupling temperature but does not represent the beginning stages of hydrogen decoupling. this may also help explain some of the earlier universe star formations. Though certainly not solve the entirety of issue of early star formation in terms of how rapidly they formed in the early universe. I will also likely examine the methodology of equation 25 of the above article and compare it to the classical Bose_Einstein, Fermi-Dirac statistics method mainly to get a feel for the deviations that may occur between the two methods. Thoughts ? pS @Sensei I seem to recall a few years back you had an examination regarding star formation. If you still have that work handy and if you feel it would relate to this I wouldn't mind looking over it again.

No the big rip requires the negative kinetic energy term to occur. However current evidence support that the big rip as being unlikely to occur as the cosmological constant shows strong supportive evidence of being constant. Provided it remains constant the heat death scenario is more likely

well piece of advise study the basic definitions and related formulas for mass, energy, and work then apply those to the EM equations that are posted in this thread. in order to properly learn physics you will want to start at the beginning and not jump somewhere in the middle. You will just confuse yourself. Also make sure your familiar with the linear and angular momentum equations those will be involved in every level of physics.

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 \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\]

To add to Lorentz Jr answer you might want to study Newtons laws of momentum https://en.wikipedia.org/wiki/Newton's_laws_of_motion there is a section there specifically on electromagnetism while your at it memorize the following statement "Mass is the resistance to inertia change" then look and see how that applies to the Laws above the reason I suggest the above is that you seem to lack in basic physics and the above applies to every physics theory. So its highly important to understand the above. for example your title Could mass be grounded by Mass makes zero sense if you apply the definition given By substitution it would read as Could resistance to inertia change be grounded by resistance to inertia change ? the answer is obviously no once to use the definition of mass, the others are doing an excellent job helping you on the EM field so I wont interfere with their progress .

support document list https://physics.nist.gov/cuu/Constants/codata.pdf Fundamental constants 2018 https://physics.nist.gov/cuu/pdf/wall_2018.pdf Cosmic inventory (2004) https://arxiv.org/abs/astro-ph/0406095 2018 Planck datasets https://www.aanda.org/articles/aa/full_html/2020/09/aa33910-18/aa33910-18.html Planck cosmological parameters 2018 https://www.aanda.org/articles/aa/pdf/2020/09/aa33910-18.pdf Equilibrium temperature of Hydrogen https://iopscience.iop.org/article/10.3847/1538-4357/ab2d2f/pdf

You would likely Sir Roger Penrose "100 roads to Reality of interest. Just an FYI so we don't derail this thread. The term you posted is commonly applied in QFT wavefunctions just an FYI

The description I typically use for fields is a collection of values under geometric treatment but yours is excellent

+1 I like that descriptive

\[{\small\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline Particle& Spin & g & Q &B&L_e &L_\mu&M (Mev)&\tau\\\hline \gamma&1&2&0&0&0&0&<3*10^{-33}&stable\\\hline e^-&1/2&2&-1&0&1&0&0.511&>2*10^{22}yrs\\\hline e+&1/2&2&1&0&-1&0&0.511&>2*10^{22}yrs\\\hline v_e&1/2&1&0&0&1&0&,5*10^{-5}&stable\\\hline \overline{v}_e&1/2&1&0&0&-1&0&<5*10^{-5}&stable\\\hline \mu^-&1/2&2&-1&0&0&1&105.7&2.2*10^{-6}sec\\\hline \mu^+&1/2&2&1&0&0&-1&105.7&2.2*10^{-5}sec\\\hline v_\mu&1/2&1&0&0&0&1&<0.25&>10^{32}yrs\\\hline \overline{v}_\mu&1/2&1&0&0&0&-1&<0.25&>10^{32}yrs \\\hline p&1/2&2&1&1&0&0&938.3&.10^{32}yrs\\\hline \overline{p}&1/2&2&-1&-1&0&0&938.3&>10^{32}yrs\\\hline n&1/2&2&0&1&0&0&939.6&898 sec\\\hline \overline{n}&1/2&2&&*-1&0&0&939.6&898 sec\\\hline \pi^0+&0&1&1&0&0&0&139.6&1.39*10^{-8}sec\\\hline \pi^-&0&1&0&0&0&0&135.0&8.7*10^{-17}sec\\\hline \pi^+&0&1&-1&0&0&0&139.6&2.6*10^{-8}sec\\\hline\end{array}}\] will have to go through and update these entries table is as follows g is degrees of freedom, electric charge Q, Baryon number B, (note need to add tau and tau neutrino for the lepton family, gauge bosons W,Z,g and Higgs as well as quarks) electron lepton number\[ L_e\] muon lepton number\[L_\mu\]

\[\array{ \mathfrak{g} \times X && \overset{R}{\longrightarrow} && T X \\ & {\llap{pr_2}}\searrow && \swarrow_{\rlap{p}} \\ && X }\] \[{\small\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline Particle& Spin & g & Q &B&L_e &L_\mu&M (Mev)&\tau\\\hline \gamma&1&2&0&0&0&0&<3*10^{-33}&stable\\\hline e^-&1/2&2&-1&0&1&0&0.511&>2*10^{22}yrs\\\hline e+&1/2&2&1&0&-1&0&0.511&>2*10^{22}yrs\\\hline v_e&1/2&1&0&0&1&0&,5*10^{-5}&stable\\\hline \overline{v}_e&1/2&1&0&0&-1&0&<5*10^{-5}&stable\\\hline \mu^-&1/2&2&-1&0&0&1&105.7&2.2*10^{-6}sec\\\hline \mu^+&1/2&2&1&0&0&-1&105.7&2.2*10^{-5}sec\\\hline v_\mu&1/2&1&0&0&0&1&<0.25&>10^{32}yrs\\\hline \overline{v}_\mu&1/2&1&0&0&0&-1&<0.25&>10^{32}yrs \\\hline p&1/2&2&1&1&0&0&938.3&.10^{32}yrs\\\hline \overline{p}&1/2&2&-1&-1&0&0&938.3&>10^{32}yrs\\\hline n&1/2&2&0&1&0&0&939.6&898 sec\\\hline \overline{n}&1/2&2&&*-1&0&0&939.6&898 sec\\\hline \pi^0+&0&1&1&0&0&0&139.6&1.39*10^{-8}sec\\\hline \pi^-&0&1&0&0&0&0&135.0&8.7*10^{-17}sec\\\hline \pi^+&0&1&-1&0&0&0&139.6&2.6*10^{-8}sec\\\hline\end{array}}\]

Any equation where the units on the LHS does not match the units on the RHS is invalid under dimensional analysis. Here for further detail http://web.mit.edu/2.25/www/pdf/DA_unified.pdf

Might help to know that in order for the cosmological constant to stay constant the. W=-1 too far from that value and it will vary over time. The options are still viable for an evolving cosmological constant but so far research is showing non evolving. If Lambda does evolve then you may have an eventual collapse as opposed to a big rip. Still going through the article however they seems to be using as negative pressure however still unclear on that myself till have a chance to better study the math. Yeah looks looks like the second terms in equation one is describing a vacuum scalar field. The positive and negative kinetic energy sign flips directly apply to that same equation. The stress tensor components in the article equation 10. The -T^00 component is the energy density term T^0_i is the mixed covariant/contravariant momentum Flux in the I direction with T^0_j being in the j direction. Just to help you better understand some of the equations in the article. Insofar as he is describing the stress momentum terms of H_{ij}. The majority of the other equations are fairly standard from thevFLRW metric including the related equations of state. Hope that helps. Edit; are you familiar with how the equations of state are derived ? That might help if the answer is no. I should also note that the article is in the Newton limit under GR and does not include quantum field theory itself (QFT equations are second order). Here is an article on first order perturbation theory as applied to QM. https://courses.physics.illinois.edu/phys485/fa2015/web/perturb.pdf

that would be great, I gathered much of details you described from the mathematics of the article I first found still going through it. Always interested in good resources, I tend to collect good examples of different field treatments so enjoy coming across ones I haven't come across before. They are always handy in model building

seems to be a bit of a glitch that the latex structures tend to drop ah well those equations are fairly straightforward to fix up.

The intended purpose will be to eventually migrate this into a full article using current cosmological parameters. Its a project I've been building towards for several years now and has always been a primary focus of my studies. Now I'd like to formalize it however evidently there is issues going on with lengthy edits as I just lost all the latex work above yet again lmao

good plan will do as much as possible

This thread will take me a considerable amount of time as I will be examining various treatments of BB nucleosynthesis and development of an eventual article of processes involved. for the initial stages I will simply be gathering the relevant formulas. Prior to symmetry Break Relevant equations The FLRW metric of the LCDM universe is used by the LCDM model of the Big bang to describe the evolution history of our Observable universe. The model starts at 10^{-43} seconds forward from a low entropy, hot dense state. One plausible explanation of how our universe began prior to that include quantum fluctuations. The model only describes our Observable portion as we do not know what occurs beyond the Cosmological event horizon. The FLRW metric is given as follows \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] where k is the curvature term, a is the scale factor both being dimensionless quantities. The contributions of each particle species via their corresponding equations of state is determines how our universe expands. The evolution history can be determines as a function of Cosmological redshift via the following equation \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] where the standard model may be represented by the covariant derivative form of the Langrangian \[\mathcal{L}=\underbrace{\mathbb{R}}_{GR}-\overbrace{\underbrace{\frac{1}{4}F_{\mu\nu}F^{\mu\nu}}_{Yang-Mills}}^{Maxwell}+\underbrace{i\overline{\psi}\gamma^\mu D_\mu \psi}_{Dirac}+\underbrace{|D_\mu h|^2-V(|h|)}_{Higgs}+\underbrace{h\overline{\psi}\psi}_{Yukawa}\] \[V_{ckm}=V^\dagger_{\mu L} V_{dL}\] The gauge group of electroweak interactions is \[SU(2)_L\otimes U(1)_Y\] where left handed quarks are in doublets of \[ SU(2)_L\] while right handed quarks are in singlets the electroweak interaction is given by the Langrangian \[\mathcal{L}=-\frac{1}{4}W^a_{\mu\nu}W^{\mu\nu}_a-\frac{1}{4}B_{\mu\nu}B^{\mu\nu}+\overline{\Psi}i\gamma_\mu D^\mu \Psi\] where \[W^{1,2,3},B_\mu\] are the four spin 1 boson fields associated to the generators of the gauge transformation \[\Psi\] The 3 generators of the \[SU(2)_L\] transformation are the three isospin operator components \[t^a=\frac{1}{2} \tau^a \] with \[\tau^a \] being the Pauli matrix and the generator of \[U(1)_\gamma\] being the weak hypercharge operator. The weak isospin "I" and hyper charge \[\gamma\] are related to the electric charge Q and given as \[Q+I^3+\frac{\gamma}{2}\] with quarks and lepton fields organized in left-handed doublets and right-handed singlets: the covariant derivative is given as \[D^\mu=\partial_\mu+igW_\mu\frac{\tau}{2}-\frac{i\acute{g}}{2}B_\mu\] \[\begin{pmatrix}V_\ell\\\ell\end{pmatrix}_L,\ell_R,\begin{pmatrix}u\\d\end{pmatrix}_,u_R,d_R\] The mass eugenstates given by the Weinberg angles are \[W\pm_\mu=\sqrt{\frac{1}{2}}(W^1_\mu\mp i W_\mu^2)\] with the photon and Z boson given as \[A_\mu=B\mu cos\theta_W+W^3_\mu sin\theta_W\] \[Z_\mu=B\mu sin\theta_W+W^3_\mu cos\theta_W\] the mass mixings are given by the CKM matrix below \[\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}\] Bose Einstein Statistics \[n_i = \frac {g_i} {e^{(\varepsilon_i-\mu)/kT} - 1}\] Fermi-Dirac statistics \[ n_i = \frac{g_i}{e^{(\epsilon_i-\mu) / k T} + 1}\] Maxwell Boltzmann \[\frac{N_i}{N} = \frac {g_i} {e^{(\epsilon_i-\mu)/kT}} = \frac{g_i e^{-\epsilon_i/kT}}{Z}\] Saha Boltzmann equation (calculate hydrogen decoupling \[\frac{n_i+n_e}{n_i}=\frac{2}{\omega^3}\frac{g_i+1}{g_i}exp[-\frac{(\epsilon_i+1-\epsilon_i)}{k_BT}\]

The ones I find frustrating are the posters that resort to insult tactics after you spend considerable time trying to correct misconceptions, explain why they are wrong, or describe something that you support with material written by professionals in a particular field. It truly does make one feel that they are literally wasting their time. In those circumstances it never seems to matter how much supportive documentations such as professional peer review material, the relevant mathematics etc you present to support your statements. In those cases I have to constantly remind myself that even when you cannot help said individual you invariably help other readers. Eventually though one has to report the individual which the moderation staff does an excellent job of cooling the situation down.

Well that's a first I never heard of Vaidya spacetime any recommended literature on it ? I spotted this article which seems to have a half decent coverage but if you are familiar with better I would appreciate it "Geometry of the Vaidya spacetime" by Armand COUDRAY & Jean-Philippe NICOLAS https://arxiv.org/pdf/2101.06544

Be well