stephaneww

Thank you for your answer. There is no emergency... Since this problem lasts a few more days, it won't change much. I forgot a step to make verification easier : [math]l_p=\sqrt{\frac{\hbar G }{c^3}}[/math] [math]l_p^2=\frac{\hbar G }{c^3}[/math] then we have : [math]\frac{\hbar.c}{l_p^2}=\frac{\hbar.c.c^3}{\hbar G}= \frac{c^4}{G}=F_p[/math]

I will try to approach the conclusion of this thread with the following. We have: - the energy density for quantum mechanics alone with J/m^3 is : [math]A = m_p c^2/l_p^3=\hbar (l_p^{-4}) c[/math] [math]=\hbar (l_p^{-2})^2 c[/math] - the formula of the energy density with [math]\hbar[/math] gives with J/m^3 in cosmology by adding the factor (8pi)^2 : [math]B = \frac{1}{(8 \pi)^2} .\hbar (\Lambda_{m^{-2}})^2 .c[/math] The energy density of the cosmological constant [math]C[/math], is the geometric average of [math]A[/math] and [math]B[/math] (A/C=C/B ) : [math]C=\sqrt{A.B}[/math] [math]=\sqrt{\hbar (l_p^{-2})^2. c.\hbar (\Lambda_{m^{-2}})^2. c /(8 \pi)^2 }[/math] [math]=\sqrt{\hbar^2 (l_p^{-2})^2.c^2 (\Lambda_{m^{-2}})^2/(8 \pi)^2 }[/math] [math]= \frac{\hbar c.\Lambda_{m^{-2}}}{l_p^2 8 \pi } [/math] [math]= \frac{F_p.\Lambda_{m^{-2}}}{8 \pi }[/math] where [math]F_p= \frac{c^4}{G}[/math] is Planck's force [math]...= \frac{c^4 .\Lambda_{m^{-2}}}{ 8 \pi G}=\rho_\Lambda c^2[/math] i.e. the classical formula of the energy density of the cosmological constant

Actually, I'm not sure: I didn't check. (I speak about T(Gy) when I said " we need more than 3 decimals.." )

😅 edit: I'm not sure I understood... Which value are you talking about ?

Yes, because I haven't [math]\Omega_r[/math] isolated. edit: after Gy > 54.532554, we need more than 3 decimals on [math]H/H0[/math] to have a correct calculation.

This point is very simple for me : nothing can be built by ignoring conventional physics. New bricks or models can be added but they must make it possible to find or refine the existing ones. I will try, by curiosity, to develop my summary description without the mathematical arguments : You opposed : The surface of the sphere, which is actually the empty volume of the universe, increases over time. As a result, the radiation and material and radiation densites decrease over time while the density of the vacuum is constant, but total Energy of vaccum increases due to the increase of the volume of the universe resulting from H. In other words, matter does not create matter but the vacuum can only be a vacuum. . I think that's correct Other point : By numeric application of the "LightCone7" table it is easily shown that [math]H^2/H_0^2[/math] calculated with all [math]\Omega[/math] is not exactly [math]H^2/H_0^2[/math] calculated with [math]H/H_0[/math] and the gap is large in the "young" universe and very small for the H "close" of us. Whether it is with [math]\Omega_0=1[/math] or [math]\Omega_0=1-\Omega_{\Lambda}-\Omega_{m}-\Omega_{r}[/math] (as a reminder, the difference is very small between these two calculations). We know [math]\Omega_{r}[/math] and [math]\Omega_{m}[/math] that we know how to measure by observation. There remains [math]\Omega_{\Lambda}[/math] that we deduce from the other measurements and from the model [math]\Lambda CDM[/math] that we don't know how to explain, and this gap also has no explanation to my knowledge. Perhaps the origin of the dark energy originates in this unexplained gap, but this remains to be demonstrated.

Thank you... But you've helped me a lot.

Ok, http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html the equality with all [math]\Omega[/math] allow to show it. ( and [math]\Omega_0=1[/math] is in input parameters ) we gave both a part of the solution : and so, for [math]\Lambda[/math], it's [math]\Omega_{\Lambda,H}[/math] in relation to [math]\Omega_{\Lambda,H0}[/math] which reflects the evolution of [math]H[/math], the latter also affecting the critical density, both by [math]H^2[/math] ... … certainly, with the exception ( very probably) of the "young" universe. Did I succeed to answer the first question of last quote in this message ( I had miss something ?) ? For 2*, in the near past period and for the whole future, this affects [math]H^2/H0^2[/math] by about 0.1%. It is reasonable to say that, in these cases, the impact is negligible, but it cannot be denied.

[math](1-\Omega_0)[/math] is close to [math]9.0267568*10^{-5}[/math]. This is the best estimate I could make for [math]H^2/H_0^2[/math] for the calculation with all [math]\Omega[/math]. However, it is only valid, with an accuracy better than 1%, for about ten lines of the table above and below the value [math]H/H_0=1[/math,] i.e. today. edit : arf, actually it doesn't change much compared to [math]1-\Omega_0=0[/math]

I'm getting closer in my spreadsheet: I have the correct formula for [math](\frac{\Omega{r,0}}{a}+\Omega_{m,0})=\frac{(1-\Omega_{\Lambda,0}-(1-\Omega_0))a^3}{1+\frac{1}{3400*a}}[/math]. I'm just missing the numerical value of [math](1-\Omega_0)[/math] to be sure of me by numerical check

You're gonna laugh. I made a mistake earlier that we both didn't see. The good equality is : [math](H/H_0)^2=\Omega_{\Lambda,H0} / \Omega_{\Lambda,H}[/math]. of course I used [math]\Lambda_{m^-2}=3H^2\Omega_{\Lambda}/c^2[/math] problem for me I didn't succes to find the value of (H/H_0)^2 with all [math]\Omega[/math] I don't want to violate the rules of the speculation section by adding a spreadsheet as an attachment. For all the formulas, I can send you the complete attachment by personal message H0 Lambda (m^-2) 67,9 1,12009E-052 2,20048913788313E-18 Om_Lambda,H H²/H0² OmL0/OmLH col I-col J H H/Ho 0,693 column D ² 22915,263 1,31973E-009 525109278,359169 525109278,359169 0,00E+00 5,042478732E-014 15740,128 2,79716E-009 247751629,456384 247751629,456384 0,00E+00 3,463598069E-014 10859,192 5,87676E-009 117922050,892864 117922050,892864 0,00E+00 2,389553404E-014 7520,218 1,22538E-008 56553678,767524 56553678,767524 0,00E+00 1,654815802E-014 5224,758 2,53864E-008 27298096,158564 27298096,158564 0,00E+00 1,149702323E-014 3639,803 5,23091E-008 13248165,878809 13248165,878809 0,00E+00 8,009346966E-015 2541,361 1,07300E-007 6458515,732321 6458515,732321 0,00E+00 5,592237276E-015 1777,702 2,19288E-007 3160224,400804 3160224,400804 0,00E+00 3,911813941E-015 1245,393 4,46807E-007 1551003,724449 1551003,724449 0,00E+00 2,740473769E-015 873,554 9,08142E-007 763096,590916 763096,590916 0,00E+00 1,922246088E-015 613,344 1,84215E-006 376190,862336 376190,862336 0,00E+00 1,349656810E-015 430,988 3,73081E-006 185750,656144 185750,656144 0,00E+00 9,483844126E-016 303,042 7,54619E-006 91834,453764 91834,453764 0,00E+00 6,668406293E-016 213,19 1,52475E-005 45449,9761 45449,9761 0,00E+00 4,691222793E-016 150,041 3,07832E-005 22512,301681 22512,301681 0,00E+00 3,301635907E-016 105,633 6,21061E-005 11158,330689 11158,330689 0,00E+00 2,324442691E-016 74,389 1,25232E-004 5533,723321 5533,723321 0,00E+00 1,636921865E-016 52398 2,52408E-010 2745550404 2745550404 0,00E+00 1,153012298E-013 36,917 0,00050848767592 1362,864889 1362,864889 0,00E+00 8,123545750E-017 26,017 0,001023808664586 676,884289 676,884289 0,00E+00 5,725012590E-017 18,342 0,002059870207846 336,428964 336,428964 0,00E+00 4,036137177E-017 12,938 0,004139986653113 167,391844 167,391844 0,00E+00 2,846992847E-017 9,137 0,008300915344211 83,484769 83,4847690000001 0,00E+00 2,010586925E-017 6,467 0,016570190934269 41,822089 41,822089 0,00E+00 1,423056325E-017 4,596 0,032807504311844 21,123216 21,123216 0,00E+00 1,011344808E-017 3,292 0,063946029182273 10,837264 10,837264 0,00E+00 7,244010242E-018 2,395 0,120815373015285 5,736025 5,736025 0,00E+00 5,270171485E-018 1,788 0,216769514886717 3,196944 3,196944 0,00E+00 3,934474579E-018 1,392 0,357647146254459 1,937664 1,937664 0,00E+00 3,063080880E-018 1,145 0,528594039015274 1,311025 1,311025 0,00E+00 2,519560063E-018 1 0,693 1 1 0,00E+00 2,200489138E-018 0,919 0,82054463798352 0,844561 0,844561 0,00E+00 2,022249518E-018 0,879 0,896923668301319 0,772641 0,772641 0,00E+00 1,934229952E-018 0,857 0,943564495288305 0,734449 0,734449 0,00E+00 1,885819191E-018 0,845 0,97055425230209 0,714025 0,714025 0,00E+00 1,859413322E-018 0,839 0,984485474932556 0,703921 0,703921 0,00E+00 1,846210387E-018 0,836 0,991563837824226 0,698896 0,698896 0,00E+00 1,839608919E-018 0,834 0,996325241964702 0,695556 0,695556 0,00E+00 1,835207941E-018 0,833 0,998718815257195 0,693889 0,693889 0,00E+00 1,833007452E-018 0,833 0,998718815257195 0,693889 0,693889 0,00E+00 1,833007452E-018 0,833 0,998718815257195 0,693889 0,693889 0,00E+00 1,833007452E-018 0,833 0,998718815257195 0,693889 0,693889 0,00E+00 1,833007452E-018 0,832 1,00112102440828 0,692224 0,692224 0,00E+00 1,830806963E-018 0,832 1,00112102440828 0,692224 0,692224 0,00E+00 1,830806963E-018 0,832 1,00112102440828 0,692224 0,692224 0,00E+00 1,830806963E-018

ok thank you is there a mistake? [math]\Omega_{\Lambda ,0}=\frac{\Lambda c^2}{3H_0^2}[/math] [math]\Omega_{\Lambda ,H}=\frac{\Lambda c^2}{3H^2}[/math] [math]H/H_0=\Omega_{\Lambda ,0}/\Omega_{\Lambda ,H}[/math], right? so :

Wich are the values of [math]\Omega_{r,0}[/math] and of [math]1- \Omega_{0}[/math] for this table ? and what is the number of step you used please ? that's for the number of step ok : 50 is the number of step edit 2 : what does the value Dparticle correspond to?

ok thank you

to make sure I'm not mistaken with the reverse : is [math]H/H_0=da/dt[/math] with [math]a=1[/math] now ? (I'm not sure of myself)

No, actually it's [math]\Omega^2[/math] that's closer to my [math](J/m^3)^2[/math] which corresponds to a [math]\rho^2[/math] : [math]\Omega^2=(\rho/\rho_c)^2=\rho^2/\rho_c^2[/math] if this is right in the context while [math]\Delta \rho^2=(\rho_1 - \rho_2)^2[/math]

It is certain that if my description makes sense, I must confront it with the standard cosmological model, and for the moment, it does not work. However, this point is in my brief description: edit : no, you're right, my description is incomplete, it doesn't describe Lambda enough I confined myself to 3 descriptions of vacuum energy density, 2 known: - the quantum vacuum in Planck units (mp.c2/lp3) which is very high to the point that when it is converted into density its value is incredible. - the vaccum of the relativist Lambda. 1 new vacuum mixing quantum and relativity with hbar and Lambda which is incredibly low. It seemed consistent to me to not mix them with other approaches of vacuum. I may have something to answer on this point later, but I agree for the moment. Of course, this document is too complex for me I noted however two unusual square on variables where I had never seen them before: [math]\Omega^2[/math] (197) page 25 and, more important, [math]\Delta \rho^2[/math] (A9) page 30 just as I had never seen [math](J/m^3)^2[/math] in the scientific literature. and thanks for the +1, it's very sympathetic .

Honestly, I have no idea..... and I understand your hesitancy on my second equation _____________________________________________________ Aparty: It's just an idea, but... We take as a base a space-time where 3D space and time are linked. Time scrolls in a positive direction, it "increases". So the 3D space also increases. By bringing space-time back to the image of the surface of a sphere, the surface of the sphere will increase with time. Assuming that this surface is the vacuum, the quantity of vacuum will increase over time while by the law of energy conservation the quantity of matter will remain stable. In the end, we will have an increasing vacuum energy and a constant mass energy. In terms of energy density, that of vacuum will prevail over that of matter. It may be a description of this type that is equated by the model [math]\Lambda CDM[/math]

I'm not expert enough to be affirmative. I the most I can offer you, it's the same formula (in [math]s^{-2}[/math] for [math]\Lambda[/math]) used by a french CNRS researcher page 10 of this document : http://www.cnrs.fr/publications/imagesdelaphysique/couv-PDF/IdP2008/03-Bernardeau.pdf edit : [math]\Omega_\Lambda \rho_c = \rho_\Lambda[/math] the adjustment is made by the variation of [math]\Omega_\Lambda[/math], right ? it's [math]\rho_\Lambda[/math] which is constant as [math]\Lambda[/math]

I understand that if we consider a universe, almost, but not flat, it modifies the critical density and so affects my result. I don't have enough knowledge to do the calculation you propose next. However, I remember reading on Wikipedia, but without being able to find out where immediately, that the universe was so close to being flat that most cosmologists considered that it was indeed flat. Is this last proposal wrong please?

edit me too : Yes, I should have said "energy critical density" ([math]J/m^3)[/math] [math]\Omega_\Lambda=\frac{\rho_\Lambda}{\rho_c}[/math] with : [math]\rho_\Lambda=\frac{c^2}{8 \pi G}\Lambda[/math] [math]kg/m^3[/math] and [math]\rho_c=\frac{3H_0^2}{8 \pi G}[/math] [math]kg/m^3[/math] so [math]\Lambda_{m^{-2}}=\frac{3H_0^2}{c^2}\Omega_\Lambda m^{-2}[/math] for the value in [math]kg/m^3[/math] if I'm not mistaken, we do : [math]\frac{F_p \Lambda_{m^{-2}}}{c^2 8 \pi}[/math] is that correct with these details ?

Uh, is this for the first message ? I used: [math]\rho_c=\frac{3c^2H^2}{8 \pi G}[/math] for critical density, is that correct? and [math]\Lambda_{m^{-2}}=\frac{3H_0^2}{c^2}\Omega_\Lambda[/math] is that correct? Is there anything more to add?

First : Thank you for your answer +1 Indeed, you're right about the second message: For H0=70,00 [math]\frac{\hbar*f}{V_u}=8.94*10^{-133}J/m^3[/math] The energy density of the cosmological constant would be for a universe age of 12.8 billion years : [math]6.44*10^{-10}J/m^3[/math] As we are in the speculation section, I will add this: Cosmologists are debating the value of H0. This could result in a modification of the standard model. (https://www.scienceforums.net/topic/119814-h0licow-new-measurements-of-hubble-constant-highlight-problem/) Among the hypotheses there would be this one : the cosmological constant would not be constant, it would accelerate the acceleration of expansion. In this hypothesis, its energy density would decrease over time, all other things being equal (if I am not mistaken) Now that we agree, i.e. that H0 does not give a constant result for a second message, let's address the first message if you agree : This time all values are constants, the results are constant, accurate and precise. The thing I'm not sure about is the conclusion to be drawn. Of course, there is an effort to be made to understand the "big piece", but if you wish, I can detail it to make it more accessible. oops, traduction of French Wikipédia : Following the precise calibration of the distance of the Large Magellanic Cloud 15, measurements made by Adam Riess using Large Magellanic Cloud cepheids in 2019 give a Hubble constant value of 74.03±1.42 kilometres per second per megaparsec16.The difference between this measurement and the value calculated by the Planck mission is due to the parameters of the cosmological model used for the calculations in the case of the Planck mission.

Oops, I got the wrong thread, sorry.

oops, I ate the powers of 10 ... correction in the quote and of course in the first message, you should read [latex]2.866*10^{-19}[/latex] and not [latex]2.866*10^{19}[/latex]