pbuk said:
Not exactly, there is a much more sophisticated treatment of dark energy. You can see the code (in R) if you go to https://cosmocalc.icrar.org/ and click the "R code" tab.JimJCW said:
pbuk said:
Rather than reverse engineer output I'd rather look at the implementations themselves. For instance the constants used in Jorrie's original model include these:JimJCW said:
// https://github.com/light-cone-calc/light-cone-calc/blob/main/src/model.ts
const physicalConstants = {
rhoConst: 1.7885e9, // 3 / (8 pi G)
secInGy: 3.1536e16, // s / Gyr
tempNow: 2.725, // CMB temperature now
convertToGyr: 1 / 978, // Convert km/s/Mpc -> Gyr^-1
};// https://github.com/joshkempner/Cosmic.NET/blob/main/Cosmic.NET/cosmo/Cosmo.cs
private const double c = 2.99792458e5; // speed of light
private const double G = 6.67259e-8; // gravitational constant
private const double KmPerMpc = 3.08567758e19;
private const double TropicalYear = 3.1556926e7; // in seconds// s_eq: 1 + 3370, // Stretch when OmegaM=OmegaR
...
//@TODO check this - should it be s_eq + 1 as the original, or as below
// from Ibix?
// const OmegaM = ((Omega - OmegaL) * s_eq) / (s_eq + 1); // Energy density of matter
// const OmegaR = OmegaM / s_eq; // Energy density of radiation
const OmegaM = ((Omega - OmegaL) * (s_eq + 1)) / (s_eq + 2); // Energy density of matterYes of course.Jorrie said:
I used yours, but it's a quick fix.Jorrie said:
Tiny but important: this was the remaining part of the problem causing the offset at z = 0.Jorrie said:
z: 0
Dnow: 3.552713678800501e-15
Dthen: 3.552713678800501e-15
Vnow: 2.460744627831758e-16
Vthen: 2.4607446278317573e-16Great stuff! I will link https://light-cone-calc.github.io/ in my signature and you can do the same, if you so wish.pbuk said:
Thanks for that, it is an unintended side effect of fixing the range so it includes z = 0 instead of z = 1e-6 for instance. I'll fix the fix.JimJCW said:
My first suspicion is the values of certain constants, particularly the conversion factor from ## km\\s^{-1}\\Mpsc^{-1} ## to ## Gyr^{-1} ## which is a simple ## \frac 1 {978} ## in LightCone8 instead of something like ## \frac{365.2421897 \times 86400 \times 1000000 \pi}{96939420213600000} ##.JimJCW said:
| z | OmegaM | OmegaL | OmegaR | OmegaT |
LightCone8 | 0 | 0.309000000 | 6.910000000 | 0.00009169139 | 1.000091691 |
From Equations | 0 | 0.308908363 | 6.91 | 0.000091637 | 1 |
Thanks, I think this is related to https://github.com/light-cone-calc/light-cone-calc/issues/6JimJCW said:
Jorrie said:
I think the error is in the UI: we should have ## \Omega_{m,0} = \Omega - \Omega_{\Lambda,0} = 1 - 0.691 = 0.309 ##.JimJCW said:
pbuk said:
I have checked the UI calculation and it seems to be right if radiation density is included, as it should.pbuk said:
Jorrie said:
rholNow = rhocritNow * Ol;
rhol = rholNow;
rhomNow = rhoNow - rhol;
rhom = rhomNow *s*s*s;
rhorNow = rhomNow/s_eq;
rhor = rhorNow *s*s*s*s;Yes, at any time, ##\rho_{0} = \rho_{r,0} + \rho_{m,0} + \rho_{\Lambda,0}##. In the case ##\Omega = 1##, this is subject to the constraint$$\rho_{0} = \rho_\mathrm{critical} = \frac{3 H_0^2 }{8 \pi G},$$pbuk said:
Yes, the same differences occur in Lightcone7, but it is calculated differently than the value in the UI. I will check that part and make it compatible, because I still feel that the value in the UI is correct.pbuk said:
Minor corrections (red) in Calculation.js required to improve the issue:Jorrie said:
George, how do the equations change in the case where ##\Omega \ne 1##?George Jones said:
I am not sure which equations you mean. ##\Omega = \Omega_r + \Omega_m + \Omega_\Lambda## is always true, as is ##\Omega + \Omega_k = 1##. If ##\Omega = 1##, then ##\Omega_k =0##, but if f ##\Omega \neq 1##, then ##\Omega_k \neq 0##.Jorrie said:
I suspect @Jorrie is suffering from the same problem as I am with the confusing terminology. I am working on increasing consistency for my rewrite:George Jones said:
omegaM - density of mass as a fraction of the critical density.omegaLambda - density of the cosmological constant as a fraction of the critical density.omegaRad - density of radiation as a fraction of the critical density.omega - total density of [stuff] as a fraction of the critical density ## \Omega = \Omega_{m} + \Omega_{\Lambda} + \Omega_{rad} ##.omegaK - Do we bother with this?omegaM0 - density of mass now as a fraction of the critical density now.omegaLambda0 - density of the cosmological constant now as a fraction of the critical density now.omegaRad0 - density of radiation now as a fraction of the critical density now.omega0 - total density of [stuff] now as a fraction of the critical density now ## \Omega_{0} = \Omega_{[m,0]} + \Omega_{[\Lambda,0]} + \Omega_{[rad,0]} ##.omegaK0 - curvature now as a fraction of the critical density now (is this actually constant in all models?) ## \Omega_{[K,0]} = 1 - \Omega_{0} ##.Common practice in cosmology is to write "something" in terms of redshift ##z##, i.e., to substitute ##s = 1 + z## for every ##s##. Common cosmological notation is ## [something] = \frac{H\left(z\right)^2}{H_0^2} =: E\left(z\right)^2##. I am not sure why.pbuk said: