The Birth Mechanism of the Universe from Nothing and New Inflation Mechanism!

[Mordred]

For the record I did look at your paper where you argued that negative pressure is invalid. My question still remains the value you give in equation 90 is the OLD cosmological problem not the new cosmological problem the old cosmological problem is called the vacuum catastrophe. The new cosmological problem is why is the value measured so low compared to the calculated OLD cosmological problem. The value you have in equation 90 is not the value measured for Lambda.

I don't agree with much your other paper either but hey if you think using the vacuum catastrophe value serves you good luck with that

the accepted professional value measured is roughly

 

6.0∗10−10joules/m3

or 10−27kg/m3

but good luck on applying ZPE to the measured value for Lambda.

After all its only 120 orders of magnitude off the mark if you want a clear demonstration of the above statement this forum had a recent other related thread on it and Migl posted an excellent video discussing the problem.

feel free to watch it 

 

 

here is Sean Caroll's coverage and no I didn't get my previous equations from this article but the article does contain them. They are well known relations that I regularly use and thus took the time to create my own set of notes how each equation of state is derived and how to use QFT to describe each as well as how the Raychaudhuri equations can also derive the first and second Freidmann equations. Some of those notes I have on this forum as a time saver.

https://arxiv.org/pdf/astro-ph/0004075

Here are the Raychaudhuri relations I mentioned.

https://amslaurea.unibo.it/18755/1/Raychaudhuri.pdf

 

Edited November 17, 2024 by Mordred

[Mordred]

 

You may find the Christoffels useful at some point in time so here if your interested. If not no worries

https://www.scienceforums.net/topic/128332-early-universe-nucleosynthesis/page/3/#findComment-1272671

Even though you believe the SM model method is wrong here is how expansion rates for H is derived 

as a function of Z.

I will let you figure out how your own personal model works from the mainstream physics That onus is yours and not mine.

 

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

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

How you choose to get your model working is your problem . I'm simply challenging your model using main stream physics and relevant questions while providing some guidance on the relevant main stream relations. What you do with them is your problem.

Particularly since you choose to not include KE or pressure to prevent gravitational collapse.

Does your theory have a critical density I have no idea might be relevant 

Here is a handy aid for the issue of expansion vs gravitational collapse 

Apply this (its how the critical density formula got derived.) Along with GR of course.

https://www.physics.drexel.edu/~steve/Courses/Physics-431/jeans_instability.pdf

In particular see equation 28 for 

\[\frac{3}{5}\frac{GM^2}{R}\]

 

Edited November 17, 2024 by Mordred

[Mordred]

Just  side note I bet I can give you a relation you never seen nor considered with regards to the Hubble parameter.

\[H=\frac{1.66\sqrt{g_*}T^2}{M_{pl}}\]

could this have anything to do with those equations of state I keep mentioning ? Ie the thermodynamic contributions of all particle species with regards to determining rate of expansion.

Maybe this will help Please explain why your other article includes the equations state and thermodynamic relations to pressure Which obviously involves kinetic energy but this article doesn't

I just do not get that though from the varying DE term that sounds more in line with quintessence which wouldn't be w=-1

 

Edited November 18, 2024 by Mordred