Questions around the LambdaCDM model and a classical mechanics model of universe

[stephaneww]

Hi,

In a post in date of November 30 I find that the mass of ordinary matter  [latex]M_b[/latex], could be determinate with the constants of the relativity (abstract's data planck 2018 used and data Planck 2015 also) :

[latex] \Large {M_b = \frac{2c^2}{G\sqrt{\pi \Lambda} }}[/latex]

 

values here 1.1056*10^-52 m^-2 and here 1.46*10⁵³kg 

 

I know it's very surprising, we'll prefer to have the mass of dark matter in addition... You might think it's a coincidence.

However we can do this other calculation 

[latex](M_b/2)*G*\Lambda *1 kg/1m^2 = 5.34*10^{-10} \text{ Joules /m^3}[/latex] 

and it's the density of the cosmological constant.

 

The thing I can't remember from school it's : what mean in physics " [latex]1kg/1m^2[/latex]" in simples words 

Another thing seems to appear : it's a explaination (limited) in classical mechanics of a description of the universe

Thanks in advance for your answers

 

Edited December 8, 2018 by stephaneww

[et pet]

16 minutes ago, stephaneww said:

The thing I can't remember from school it's : what mean in physics " 1kg/1m2" in simples words 

1 Kilogram Per 1 Square Meter 

Edited December 8, 2018 by et pet

[stephaneww]

2 minutes ago, et pet said:

" Kilograms Per Square Meter "

That's his definition, but his sense physic here?

Edited December 8, 2018 by stephaneww

[stephaneww]

On ‎08‎/‎12‎/‎2018 at 2:41 PM, stephaneww said:

That's his definition, but his sense physic here?

To start let's look for the value of [latex]M_b[/latex] with wikipedia data :

[latex]\Large{M_b=\frac{2*299792458^2}{6.67408*10^{-11}* \sqrt{\pi*1.1056*10^{-52}}}}=1.445*10^{53}kg \text{ versus }1.46*10^{53}kg = \text{ data wikipedia}[/latex]

 

Then break down the formula 1 kg / m ^ 2 to find in step its physical sense :

[latex] a [/latex] is an acceleration.

[latex] a=(M_b/2)*G*\Lambda=(1.445*10^{53}/2)*6.67408*10^{-11}*1.1056*10^{-52}=5.3317*10^{-10}m/s^{-2}[/latex]

for a unit of mass M₁, the force is F=M₁*a = 5.3317*10^-10 N (1N= 1kg*1m/1s²)

per m² we have a pression p=F/m²=5.3317*10-10 N/m² (1N/m²= 1kg*1m^-1*1s^-2=1j/m³)

 

The density of the vacuum energy of the cosmological constant =

[latex]\Large{\rho_\Lambda*c^2=\frac{c^4 \Lambda}{8*\pi G}=\frac{299792458^4*1.1056*10^{-52}}{8*\pi*6.67408*10^{-11}}}=5.3241*10^{-10}J/m^3[/latex]

The difference is 0.15%

 

With data 2015 the difference is  0.13%

 

I don't know how to justify theses steps, but the accuracy of the numerical value is remarkable

I think it validates the definition of baryonic material mass from the relativity constants.


What is your opinion, please

 

 

 

Edited December 14, 2018 by stephaneww

[stephaneww]

Another remarkable relationship, about baryonic matter and factor 2, with correct dimensions this time with data mission Planck 2018  (table 2, page 15, last column):

1.in ΛCDM model :

radius universe observable : [latex]R=4,358*10^{26} m[/latex]

Hubble constant [latex]H_0=67.4km/s/Mpc=2.184*10^{-18}s^{-1}[/latex]

baryon density : [latex]\Omega_b=0.04936[/latex]

___________________________________

[latex]A=R^2*H_0^2*\Omega_b=(4,358*10^{26})^2*(2.184*10^{-18})^2*0.04936=4,4727*10^{16} m^2 s^{-2}[/latex]                                =

2. in quantum mechanics :

[latex]B=l_p^2/t_p^2=c^2=8.988*10^{16}m^2 s^{-2}[/latex]

___________________________________

[latex]B/A*2=1.005[/latex]

the difference is 0.5%

There could be something important with factor 2 on the mass of baryonic matter

 

note: I began by calculating the surface of a sphere of radius R and the surface of a Planck sphere; this shows the factor 8pi in relativity

 

 

 

Edited December 25, 2018 by stephaneww

[stephaneww]

The numerics values that  I give in the last post aren't exactly from the data Planck mission 2018. With the numerics value from data Planck mission 2018, the difference is always 0.5%

Edited December 26, 2018 by stephaneww