  # stephaneww

Senior Members

423

• #### Days Won

1

stephaneww had the most liked content!

## Community Reputation

19 Neutral

• Rank
Molecule
• Birthday 10/02/1968

## Profile Information

• Location
France
• Favorite Area of Science
cosmology

## Recent Profile Visitors

4587 profile views

• ### Mordred

1. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

how to explain then that rho_c * c^2 = [M L^-1 T^-2] has the dimension of a pressure? where is the error?
2. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

we can give it the dimension of a pressure by multiplying by c^2
3. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

Okay, if the radiation is missing from rho, it makes the cross-reference a lot harder to check.(if I understand what you are saying). For H=67.74 (input) I have rho_c=8.61916 10^-27 kg/m^3, against rho_c=8.62765 10^-27 kg/m^3 in the calculator I'm really uncomfortable with state equations.🙄
4. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

I confess I don't really understand. rho depends theoretically only on H? but we don't find it for H input nor for H ouput. I kept this value
5. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

Hum, I don't known if that calculator is ok for all datas : for example H input (=67.74) isn't H output, and there's a little discrepancy I don't understand about rho. $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&T (Gy)&H(t)&rho, kg/m^3&OmegaL&OmegaT \\ \hline 1.09e+3&3.70793e-4&1.55837e+6&4.61214e-18&1.28867e-9&1.00e+0\\ \hline 3.39e+2&2.48188e-3&2.47284e+5&1.16132e-19&5.11790e-8&1.00e+0\\ \hline 1.05e+2&1.52326e-2&4.16481e+4&3.29421e-21&1.80424e-6&1.00e+0\\ \hline 3.20e+1&8.97471e-2&7.17048e+3&9.76466e-23&6.08678e-5&1.00e+0\\ \hline 9.29e+0&5.20128e-1&1.24469e+3&2.94228e-24&2.02004e-3&1.00e+0\\ \hline 2.21e+0&2.96640e+0&2.23251e+2&9.46559e-26&6.27909e-2&1.00e+0\\ \hline 0.00e+0&1.37737e+1&6.74009e+1&8.62765e-27&6.88894e-1&1.00e+0\\ \hline -6.88e-1&3.29612e+1&5.63238e+1&6.02483e-27&9.86506e-1&1.00e+0\\ \hline -8.68e-1&4.78813e+1&5.59720e+1&5.94981e-27&9.98945e-1&1.00e+0\\ \hline -9.44e-1&6.28349e+1&5.59450e+1&5.94406e-27&9.99911e-1&1.00e+0\\ \hline -9.76e-1&7.77911e+1&5.59427e+1&5.94357e-27&9.99993e-1&1.00e+0\\ \hline -9.90e-1&9.27477e+1&5.59428e+1&5.94360e-27&9.99988e-1&1.00e+0\\ \hline \end{array}}$$ ... and there is this after PLANCK 2015 : https://en.wikipedia.org/wiki/Planck_(spacecraft)#2018_final_data_release
6. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

This is the case we find the formula of the critical density (*c^2 to have J/m^3) with a factor 3, so it works with the evolution of $H$ in time The method for finding $B'$ (Hubble constant) is the same as that used to determine the hypothetical $B$ (cosmological constant) value here: https://www.scienceforums.net/topic/122453-an-attempt-to-approach-a-notion-of-solubility-in-cosmology-to-explain-the-cosmological-constant/ In short, the method seems reproducible. My question therefore concerns the validity of this hypothesis. demonstration : $A=\frac{c^7}{G^2 \hbar}$ $B'=\frac{1}{(8 \pi)^2}(\frac{H^2}{c^2})^2\hbar c$ $A B'=\frac{c^8}{(8 \pi)^2 G^2}\frac{H^4}{c^4}$ $A B'=\frac{c^4 H^4 }{(8 \pi)^2 G^2}$ $3 \sqrt{A }\sqrt{B'}=\frac{3 H^2 c^2}{8 \pi G} = \rho_c c^2$ https://en.wikipedia.org/wiki/Friedmann_equations#Density_parameter (the c^2 factor for the critical density differs between the French and English versions of wikipedia, hence a small float on this point)
7. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

Okay, thanks. But that's not what I'm asking about. My question is: can this new application of dimensional analysis of my hypothetical value $B$ in QM of the cosmological constant be validly duplicated for $B'$ with the Hubble's constant ? In view of the result, I think yes. Otherwise for the actual measurement of the critical density, it seems to me that at each measurement, we are either very slightly above or very slightly below.
8. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

Hello, Mordred. I believe you're asking what we covered on pages one and two of this thread, aren't you? https://www.scienceforums.net/topic/118858-the-solution-of-the-cosmological-constant-problem/#comments Otherwise I don't know what you're talking about for the moment, can you please specify (here I parallel the evolution of the total critical density with the approach of my previous solution : square root of Planck's energy density)
9. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

oops error in the first post : Read $H_0^2 c^{-2}$ instead of $H_0 c^{-2}$ Let's consider $H_0$ the Hubble parameter (or Hubble constant) in $s^{-1}$. We want a dimension in $L^{-2}$ to replace $\Lambda_{m^{-2}}$. So we'll write $H_0^2 c^{-2}$ instead of $\Lambda_{m^{-2}}$ to get $B'=\frac{1}{(8\pi)^2} \hbar (H_0^2/c^2)^2.c$, "an energy density of Planck's universe for $H_0$". Let's consider $\rho_c=\frac{3 c^2 H_0^2}{8\pi G}$ the critical density of the universe for $H_0$. We have $3 \sqrt{A} \sqrt{B'}=\rho_c$ for a quick demonstration we'll use $A=\frac{c^7}{G^2 \hbar}=m_p c^2/l_p^3 \text{ } J/m^3$
10. ## Confirmation and generalization of my solution to the problem of the cosmological constant ??

Hi, In this thread: https://www.scienceforums.net/topic/122453-an-attempt-to-approach-a-notion-of-solubility-in-cosmology-to-explain-the-cosmological-constant/, I proposed a mathematical solution to the cosmological constant problem. However, I have not found a physical explanation. Failing that, I found a generalization of this solution to the whole universe to validate a hypothesis that had been made in this solution In this it is, it seems to me, a confirmation (and perhaps help to understand the problem of the cosmological constant?). The energy density of the quantum vacuum in Planck units is: $A=m_pc^2/l_p^3=\hbar(l_p^{-2})^2.c$ I, on the other hand, found this unknown hypothetical quantum energy density of cosmological constant : $B=\frac{1}{(8\pi)^2}\hbar(\Lambda_{m^{-2})^2.c}$ and demonstrated that the cosmological constant $C= \sqrt{\hbar(l_p^{-2})^2.c} \sqrt{ \frac{1}{(8\pi)^2} \hbar(\Lambda_{m^{-2 }})^2.c}=\sqrt{A} \sqrt{B}$ Let's consider $H_0$ the Hubble parameter (or Hubble constant) in $s^{-1}$. We want a dimension in $L^{-2}$ to replace $\Lambda_{m^{-2}}$. So we'll write $H_0 c^{-2}$ instead of $\Lambda_{m^{-2}}$ to get $B'=\frac{1}{(8\pi)^2} \hbar (H_0/c^2)^2.c$, "an energy density of Planck's universe for $H_0$". Let's consider $\rho_c=\frac{3 c^2 H_0^2}{8\pi G}$ , the critical density of the universe for $H_0$. We have $3 \sqrt{A} \sqrt{B'}=\rho_c$ The method of dimensional analysis for application in quantum mechanics of general relativity data operates again...
11. ## An attempt to approach a notion of solubility in cosmology to explain the cosmological constant

Thank you. I'll look for other cases where we'd have square root energy densities
12. ## An attempt to approach a notion of solubility in cosmology to explain the cosmological constant

I have no idea where I'm going.I don't even know if it's applicable, although this encourages me to say yes ( cosmological constant seen as a perfect gas with a negative pressure) : But it's going to be very complicated and the finalization of this project is more than uncertain. I don't know the solubility issues at all and I don't know if scalar and vector aspects are involved in this potential approach. I just want to know if at first glance it seems completely silly or if it's worth trying to find out more about it.
13. I've got it. It's just $\frac{1}{t_p^2\Lambda_{s^{-2}}}$ or $\frac{1}{l_p^2\Lambda_{m^{-2}}}$, whatever you want. The factor is $8\pi$.
14. done here : https://www.scienceforums.net/topic/122453-an-attempt-to-approach-a-notion-of-solubility-in-cosmology-to-explain-the-cosmological-constant/
×