Hello

for H0=67.66 km/s/Mpc i.e. t_H = 4.5606*10¹⁷s, and ΩΛ = 0.68694 we have:

ρ_c,tH = 3 / (8 π G t_H²) = 8.5988 * 10^-27 kg/m3.

- by dimensional analysis, looking for the value of the cosmological constant Λ of dimension m^-2 and with a mixture of relativity, deterministic Planck units we have:

 Λ = 8π ΩΛ ρ_c,_tH l_p / m_p = 1.1026 * 10^-52 m^-2.

[math]\Lambda = 8 \pi \Omega_{\Lambda} \rho_{c,t_H} \frac{l_p}{m_p}=1.1026 *10^{-52} m^{-2}[/math]

- This is exactly the value of the cosmological constant of the ΛCDM model. The formula of the density of the" quantum vacuum" at our time t_H0, seems to correspond to the formula of the density of the quantum vacuum at the time t_p.

This comes from a toy model, whose only values we can be sure of are t_p and t_H thanks to the ΛCDM model. Is this an acceptable solution to the cosmological constant problem . (???) we have the quantum field theory energy with this equality :

 

8π/3 ρ_c,tp l_p / m_p = 3.8281 * 10⁶⁹ m-2 =lp^-2

[math] \frac{ 8 \pi}{3} \Omega_{\Lambda} \rho_{c,t_p} \frac{l_p}{m_p}=3 8281.*10^{69} m^{-2}[/math]

 

 note that mp / lp is the Planck linear mass.

 

 

Edited March 28, 20214 yr by stephaneww

Hello and Hum

... it is nice to calculate:

Ω_Λ,t_H = 3 Λ c² t_H²

with t_H= Planck time : 5.391247*10^(-44) s

c = 299792458 m/s

and Λ = 1.102 * 10^(-52) m^-2

Ω_Λ,t_p= 9.60 * 10^-123

we make:

(1 / Ω_Λ,t_p)* 8 π / 3 = 8.73 * 10¹²²

to have the value of the vacuum catastrophe:

(with vacuum energy value in QFT = lp^(-2) = 3.83 *10^(69) m^-2

 

8 π * 3.83 *10^(69) / 1.105 * 10^(-52) = 8,73 * 10^(122)

 

basically the vacuum catastrophe would be the density parameter of dark energy at Planck time in the ΛCDM model and that would be no problem.

Does it make sense or not ?

 

Edited April 26, 20214 yr by stephaneww

ooops big error sorry and it's why I think have no anwsers :

read :

Ω_Λ,t_H = 1/3 Λ c² t_H²   and not Ω_Λ,t_H = 3 Λ c² t_H²  , t_H= 1/H Hubble's constant

with t_H= Planck time : 5,391247*10^(-44) s

c = 299792458 m/s

and Λ = 1,102 * 10^(-52) m^-2

Ω_Λ,t_p= 9,60 * 10^-123

we make:

(1 / Ω_Λ,t_p)* 8 π / 3 = 8,73 * 10¹²²

to have the value of the vacuum catastrophe:

(with vacuum energy value in QFT = lp^(-2) = 3,83 *10^(69) m^-2)

l_p =1,616255*10^(-35) m

and this small one error too :

8 π * 3,83 *10^(69) / 1,102 * 10^(-52) = 8,73 * 10^(122)

and not :

8 π * 3.83 *10^(69) / 1.105 * 10^(-52) = 8,73 * 10^(122)

so now are you agree with :

"basically the vacuum catastrophe would be the density parameter of dark energy at Planck time in the ΛCDM model and that would be no problem."

Please ?

EDIT :

more easy :

Ω_Λ,t_p = 1/3 Λ c² t_p²

 

vacuum catastrophe = Λ / l_p^-2 = Λ l_p²

l_p = c tp

so

vacuum catastrophe = Λ c² t_p2

vacuum catastrophe = 3 Ω_Λ,t_p

 

Edited April 28, 20214 yr by stephaneww