I LightCone Calculator Improvements

[Jorrie]

I don't know the ICRAR calculator. I see it can produce graphs, but numerically it looks like a very advanced one-shot-z calculator of professional quality and accuracy. I think one-shot makes things considerably easier and faster.

Lightcone8's algorithm can possibly be more optimized, but for its intended purpose, as a relatively easy to use educational tool, I doubt if it is worth the effort needed for pursuing the ultra-high-z regime.

 

[pbuk]

I seem to remember the ICRAR calculator changes the model to radiation only for very early redshifts, as Burt suggested a few posts back. There are a few other differences that may be worth investigating, and one thing that definitely needs looking at is the target error for the integration. This all needs work at a lower level than via the LightCone GUI so if you are interested I suggest you set up a NodeJS development environment and play with the underlying model which lives at https://github.com/cosmic-expansion/cosmic-expansion-js.

 

[JimJCW]

I seem to remember the ICRAR calculator changes the model to radiation only for very early redshifts, as Burt suggested a few posts back.

I wouldn’t say that the ICRAR calculator changes the model to radiation only for vert early redshifts. Instead, I would say that for high z values, the radiation term becomes dominating in both the ICRAR calculator and LightCone8:

By the way, where can I find Burt’s post?

@Jorrie

 

[JimJCW]

I don't know the ICRAR calculator. I see it can produce graphs, but numerically it looks like a very advanced one-shot-z calculator of professional quality and accuracy. I think one-shot makes things considerably easier and faster.

The ICRAR result shown in Post #90 suggests that the computation time using that calculator remains the same even for z = 10⁵⁰, but using LightCone8, it increases by a factor of 10 when z = 10⁶. It is a little peculiar, but not crucial.

Taking your result into consideration, we can use ‘zupper > zlower to 300000’ as permitted range for Upper row redshift. At z = 300000, Ω_R,0 already becomes very dominating (see Post #93).

@pbuk

 

[Jorrie]

Taking your result into consideration, we can use ‘zupper > zlower to 300000’ as permitted range for Upper row redshift. At z = 300000, ΩR,0 already becomes very dominating (see Post #93).

I have left z_upper at 1e6, but included a recommendation for 3e5. There is also an indicator that the integration is running for those up to 1e6 values.
http://jorrie.epizy.com/docs/index.html?i=1
This link will remain the same from one X version to the next. When we accept the version as valid, we can bump it up to the main branch.

 

[pbuk]

I wouldn’t say that the ICRAR calculator changes the model to radiation only for vert early redshifts.

I don't see how you can establish that by looking at the outputs, you need to inspect the code which you can see by clicking the "R Code" tab on the ICRAR site (although it may actually be the code at https://github.com/asgr/celestial/blob/master/R/cosgrow.R). Having said that, it does look as though it doesn't change the integrand for high z.

As I say if you want to investigate what is causing the slowdown you need to work with the underlying model and try adjusting the epsilon parameter to the integration which controls relative error and is currently set to $10^{-8}$, and also look at the full return value from the integrator to see the number of steps that are taken.

None of this is near the top of my priority list because I believe the current code achieves the objectives for the LightCone application.

 

[JimJCW]

I don't see how you can establish that by looking at the outputs, you need to inspect the code which you can see by clicking the "R Code" tab on the ICRAR site (although it may actually be the code at https://github.com/asgr/celestial/blob/master/R/cosgrow.R). Having said that, it does look as though it doesn't change the integrand for high z.

As I say if you want to investigate what is causing the slowdown you need to work with the underlying model and try adjusting the epsilon parameter to the integration which controls relative error and is currently set to $10^{-8}$, and also look at the full return value from the integrator to see the number of steps that are taken.

None of this is near the top of my priority list because I believe the current code achieves the objectives for the LightCone application.

In Post #22, it is demonstrated that the calculation results from Lightcone8 and ICRAR are consistent for z = 0.02. A similar conclusion can be reached for z = 300000:

	LightCone8​	ICRAR​
z	300000	300000
Scale (a)	3.33332222E-06	3.33332222E-06
T Gyr	8.34828635E-09	8.34837088E-09
R Gpc	5.10964255E-09
Dnow Gpc	1.41602035E+01	1.41602035E+04
Dthen Gpc	4.72005209E-05	4.72005209E-02
DHor Gpc	5.10964255E-09
Dpar Gpc	5.12398784E-09
Vgen/c	2.89051673E+03
Vnow/c	3.19580877E+00
Vthen/c	9.23753872E+03
H(z)	5.86719042E+10	5.86719042E+10
Temp K	8.17646726E+05
rho kg/m3	6.46598880E-09	6.46643447E-09
OmegaM	1.11671814E-02	1.11671814E-02
OmegaL	9.16135695E-19	9.16135695E-19
OmegaR	9.88832819E-01	9.88832819E-01
OmegaT	1.000000000E+00	1.000000000E+00

This result suggests that the ICRAR calculator uses all three parameters, Ω_m, Ω_Λ, and Ω_R even for high z values, just like LightCone8.

I have been a happy user of LightCone calculator(s) and am now very happy with LightCone8.

I think we are only trying to tighten some loose ends, right?

@Jorrie

 

[Jorrie]

I think we are only trying to tighten some loose ends, right?

Yup and at the same time we have opened the range of usability quite a bit. Lightcone7 was limited to z_upper of 20,000. With Lightcone8 we are now confident with _upper of 300,000 and 1,000,000 at a stretch (1 year age).

Plus the future expansion capability has doubled and we have an accurate cosmological horizon calculation value that many calculators lack.

Team effort paying off... Thanks guys

 

[JimJCW]

Hi @Jorrie,

What is the status of LightCone8 Cosmological Calculator (v8.3.x) at http://jorrie.epizy.com/docs/? It still gives incorrect Dhor (Ro and Dhor overlap):

Please see Post #69.

 

[Jorrie]

Hi @Jorrie,

What is the status of LightCone8 Cosmological Calculator (v8.3.x) at http://jorrie.epizy.com/docs/? It still gives incorrect Dhor (Ro and Dhor overlap):

View attachment 313696

Please see Post #69.

It may just be a cashed issue, because for me it gives:

 

[JimJCW]

It may just be a cashed issue, . . .

You are right. It works for me too.