stephaneww

Normally the energy density of the cosmological constant should be the point M

I have no idea at the moment. Maybe because the time is sinusoidal this hypothesis is based on the geometric representation of the geometric mean of Wikipedia. (time go from C' to A ?) as a reminder, it is this average that is used to solve the problem of the cosmological constant but I don't know how to develop this hypothesis more precisely at the moment. perhaps you can help me ?

I'm not sure I understand. Can you put down the numerical values, please? You are correct. This gives a universe age maximum of about 5.23*10^22 years I have no idea at the moment. what is its formula, please? ... and what is its value to check that I'm not going to make a mistake?

o I may have found a very nice numerical and literary conclusion. The simplest part first: There is a time in the evolution of the universe when the density parameter of the cosmological constant would be greater than 1 while keeping the model [math]\Lambda CDM[/math] The end of the current universe would occur when the density parameter of the cosmological constant is equal to 9*10^24 and it has an age of about [math]3.04*10^{24} \text{ years}[/math]. The most likely scenario is that it will return to its initial state after a scenario similar to quantum cosmic inflation (to be defined because I have no expertise in this field...) before starting a new Big Bang again. The numerical application now, a little difficult to follow I must admit: I will use this 2018 data from the Planck collaboration - [math]H_0=67.66 km/Mpc=1.874*10^{-11}s^{-1}[/math] - [math]\Omega_\Lambda=0.6889[/math] that give: - [math]\Lambda =1.106 m^{-2}[/math] - [math]\rho_{\Lambda,0}=5.324*10^{-10}J/m^3[/math] So we will have: - [math] D=6.118*10^{-113} J/m^3[/math] that gives us: - [math]H_\text{p,minimum}= ( \frac {D.(8* \pi)^2} { \hbar.c^{3}})^{0.5*0.5}=6,073^{-31}s^{-1}[/math] - [math]\rho_\text{c,at H(p,minimum)}=\frac{3c^2 H_\text{p,minimum}^2}{8 \pi G}=5.985*10^{-35}J/m^3[/math]- - [math]\Omega_\Lambda \text{at H(p,minimum)}=\frac {\rho_{\Lambda,0}} {\rho_\text{c,at H(p,minimum)}}= \frac{5.324*10^{-10}}{5.985*10^{-35}}=8,981*10^{24}[/math] This value is incomprehensible for the moment, it should be at most equal to 1. the Ned Wright calculator gives an observable radius of the universe [math]R_{max}=604568.8 Mpc=1.866*10^{28}m[/math] and [math]V_{max}=2.719*10^{85}m^3[/math] we have for these limit values: Total energy [math]E_{tot, end}[/math] of the current universe at the end of its life (there is only the dark energy left that bathes the entire volume of the universe): - [math]E_{tot, end}=V_{max}.\rho_\text{c,at H(p,minimum)}.\Omega_\Lambda \text{at H(p,minimum)}=[/math] - [math]E_{tot, end}=1.612*10^{51}.\Omega_\Lambda \text{at H(p,minimum)}=1.448*10^{76}J[/math] So at the end of the universe's life there remains a huge reservoir of ready energy (1,448*10^{76} Joules) to be used for a new Bing Bang. In addition, we have: - [math]V_{max}. \rho_\text{c,at H(p,minimum)}.c.\pi=1.364*10^{85} J.m/s[/math] and - [math]V_{max}/1.364*10^{85}= 2.719*10^{85} / 1.364*10^{85}=\frac{1}{1.994} .s.J^{-1}m^{-1}[/math] In other words, at the end of its life cycle, the universe would be in a quantum state of phase transition comparable to cosmic inflation, which would bring it back to a new era of Planck. If this scenario is validated, you will certainly find a simpler drafting and probably complementary to what is developed in this post "Nothing is lost, nothing is created, everything is transformed", Lavoisier, reformulation of a sentence by the Greek philosopher Anaxagoras "Let there be light...."

what I'm preparing is more precise and leads to an interesting conclusion. otherwise I saw on wiki: end of inflation between 10^-33 s and 10^-32 s I can't find it right away.

Oh, I found a very nice numerical and literary conclusion. As soon as I can, I do translating and formatting Latex

Um I think you'll have to guide me once again for a new apprenticeship....

I note simple that if we do the same calculation for 10^113 J/m^3 we have an age of 5.6*10^-32 s (edit : is this close to beginning or the end of the inflation period please?)

Probably yes. I don't actually know Hp,minimun is a speculative value How do we get the value you're talking about please ?

yes, but this remains in the order of magnitude of Planck's length and time units.

Finally, I think that with this solution, we can, perhaps, learn something more with the domain of quantum cosmology: we have with [math]\Lambda_{s^{-2}}=\Lambda_{m^{-2}}.c^2[/math] [math]D=\hbar. ({\Lambda_{m^{-2}}})^2*c/(8*\pi)^2=6.196*10^{-133}kg*m^{-1}*s^{-2}[/math] [math]D=\hbar. ({\Lambda_{s^{-2}}})^2.c.c^{2}/(8*\pi)^2=6.196*10^{-133}kg*m^{-1}*s^{-2}[/math] [math]D=\hbar.(\Lambda_{s^{-2}})^2 c^{3}/(8*\pi)^2=6.196*10^{-133}kg*m^{-1}*s^{-2}[/math] [math]D=\hbar.(\Lambda_{s^{-2}})^2 c^{3}/(8*\pi)^2=6.196*10^{-133}kg*m^{-1}*s^{-2}[/math] [math] \Lambda_{s^{-4}}=\frac{D.(8*\pi)^2}{\hbar.c^{3}}[/math] so and if I am not mistaken in simplifying [math]\Lambda_{s^{-2}}=( \frac {D.(8\pi)^2} { \hbar c^{3} })^ {0.5}[/math] assuming that there is a relationship between [math]\Lambda_{s^{-2}}[/math] and [math]H_{p,minimun}[/math] we have [math]H_{p,minimum} = ( \frac{D.(8\pi)^2} {\hbar .c^{3} } )^{0.5*0.5}=6.2*10^{-31}s^{-1}[/math] or about 3.04*10^24 years. under condition of verification, we can deduce [math]\Omega_{\Lambda ,max}[/math] and consider scenarios at this age of the universe

Thank you. From then on it becomes out of my scope in terms of mathematical knowledge Thank you for everything.

oops mistake

what is the notation [math]\phi[/math] for Planck's force field, please? if you give me his latex script as well, that would be great.

Thank you. Other question : I just readed on Wikipédia : My proposition is equivalent, no ?

okay thank you. I searched for the value of the Planck field, in French and English, but I have only one source (so I can't cross-reference): in this document: http://www.spirit-science.fr/Matiere/phys4-electrodynamique.html#mozTocId491541 at the end of the paragraph "Le champ du point zéro de l'électrodynamique stochastique" I read : "Il reste cependant un facteur multiplicatif indéterminé, C. Nous verrons un peu plus loin que des mesures expérimentales ont permis de déterminer sa valeur. Il est égal à h/2. Avec cette valeur, on retrouve précisément le champ de la deuxième formulation de Planck." translation into English: "However, there is still an undetermined multiplicative factor, C. We will see a little later that experimental measurements have made it possible to determine its value. It is equal to h/2. With this value, we find precisely the field of Planck's second formulation." so is this value correct, please: ?

No, you're right: no connection, I got out of line. Unless I'm mistaken, the relationship between [math]\phi_p[/math] and ϕ is a multiplication with, [math]\phi_p=h/2[/math] Planck fields and ϕ, the value of Planck's force if I understood what you suggest. Both, as scalar values, are dimensionless. Correct please ?

even if I don't know how to understand it, as it is authoritative, I accept the evidence. let's put this question aside for now please, I don't have the mathematical tools to try to show somthing (i think about the [math]\phi[/math] in particular and their use). Okay, thank you very much. I can't imagine how many PDF you have . This not urgent

Um, I may go too far, but I'm still going to go forward: I think this solution is a basis for unifying relativity and quantum mechanics

I don't think I would have the knowledge to go as fast as you or other science professionals on the subject of quantum fields and inflation with our model. In any case, it will always go faster than with me alone if someone is interested. Here is what I propose for the rest of this thread: or you let others do the research. or you do it in a dedicated thread so that I can try to understand where it leads you. ... and you continue, in this thread or another, the lesson on the fields if you accept. I think I understood the equality of 1.10.1 I am missing the latex writings of components and applications such as, for example, in a 3D Cartesian space Note: I do not see any error in my proposal for the "try of conclusion" solution, so I think it is correct. You will confirm or not when you have time.

All right. Thank you. Two questions before I try to sleep, to make things clear in my mind : 1- Have I proposed a correct solution to the cosmological constant problem ? 2 - if so, did it allow you to open a link with cosmic inflation via the scalar fields ?

Thank you for the welcome whith the link Well, I have read and understood up to and including 1.8.1, 1.9 and 1.10.1 However, I am not yet familiar, for moment, with the equations of 1.10.1 Would I need anything else for what we're talking about ? Thanks to the online translation.

Thank you but I'm not enought good in english to unterdestand. I'll try to find the same in french.

Um, I think I understand. It would seem to say that I put my finger on something ? Ok thanks edit if I understand you would like to use ϕ instead [math]\Lambda[/math] ?

I admit I don't understand the justification you're putting forward. I don't know what it is. Not sure that it is in my current mathematical competences. edit : Okay, I just figured it out thanks to Wikipedia. What is this symbol please : ϕ ?