Timeline for Are my assumptions about universe thermodynamics right?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 8, 2022 at 2:11 | comment | added | Aslan Monahov | Let us continue this discussion in chat. | |
| Oct 7, 2022 at 17:15 | vote | accept | Aslan Monahov | ||
| Oct 7, 2022 at 17:15 | comment | added | Aslan Monahov | amazing thanks! | |
| Oct 7, 2022 at 17:14 | comment | added | Sten | Sure but then you get the time as measured in inverse eV | |
| Oct 7, 2022 at 17:12 | comment | added | Aslan Monahov | but in plank system $\hbar$ and $c$ equals to one anyway | |
| Oct 7, 2022 at 17:11 | comment | added | Sten | Neglecting $g_*$, $g_{*s}$, and the prefactors: wolframalpha.com/input?i=planck+mass*c%5E2+%2F+%2810%5E20+eV%29%5E2+*+%28planck+constant%2F%282pi%29%29 | |
| Oct 7, 2022 at 16:51 | comment | added | Aslan Monahov | but after integrating I am getting too big values to be real: $$\rho=g\dfrac{\pi^2}{30}T^4;\quad H^2=\dfrac{8\pi\rho G}{3}=\dfrac{8\pi^3}{90M_{pl}^2}gT^4\Rightarrow \dfrac{1}{H}=\dfrac{0,6 M_{pl}}{\sqrt{g}T^2}$$ $$t(T)=0,6M_{pl}\int_T^{\infty}\dfrac{dT}{T^3\sqrt{g}}$$ and for $M_{pl}=1,2\cdot 10^{28}eV$ and $T=10^{20}eV$ I am getting $t=10^{-13}s$ that's is a lot bigger than real $\sim10^{-30}s$ | |
| Oct 7, 2022 at 16:09 | comment | added | Aslan Monahov | Ok I probably understood it came from assumption that g=const that is not true so I have to integrate anyway | |
| Oct 7, 2022 at 15:21 | comment | added | Sten | I suggest rethinking where $\rho=\frac{3}{32Gt^2}$ comes from. | |
| Oct 7, 2022 at 13:56 | comment | added | Aslan Monahov | can I just write without integrating $$\rho=g\dfrac{\pi^2}{30}T^4;\quad \rho=\dfrac{3}{32Gt^2}$$ and so $$T^2t=\sqrt{\dfrac{3\cdot 30}{\pi^2 g\cdot 32G}}=f(g)$$ where g is constant for different time intervals? For ex: $$1GeV>T>100MeV: g(T)=61,75$$ $$100MeV>T>1MeV: g(T)=10,75$$ | |
| Oct 7, 2022 at 13:43 | comment | added | Sten | That should be a sufficient approximation. There is a tricky point around $g_{*s}(T)$ being discontinuous when you want to change variables to $a$ (e.g. a jump in $g_{*s}$ as a function of $T$ doesn't imply a jump in $g_{*s}$ as a function of $a$, or alternatively the Jacobian $da/dT$ involves a delta function), but that probably won't matter much unless you're evaluating the time right after a phase transition (when $g_{*s}$ jumps). | |
| Oct 7, 2022 at 12:49 | comment | added | Aslan Monahov | I am very happy that you answered me, you probably saved me from expulsion. So I just have to break my integral into several parts with different g in history? | |
| Oct 7, 2022 at 11:30 | history | answered | Sten | CC BY-SA 4.0 |