Additional validation test for ray-tracing implementation

[dlanzieri]

We implemented a new test to validate our raytracing implementation.
Instead of running the N-body simulation, the snapshots at different scale factors are generated by using the same linear power spectrum at the scale factor a=0.5229969 (with the order set to 1).
The following image shows a comparison between the Jax-cosmo linear power spectrum (dashed line) and the 3D Power spectrum computed for each snapshot :

Then, we exported the lens planes, created the Convergence map and computed the angular power spectrum from it. The final angular power spectrum is obtained averaging over 20 samples. We also tried to investigate the behaviour of the angular power spectrum for large scale for different values of the field and Box size.

In particular we adopted the following setting:

1. Number of lens = 22 (or 11 for Boxsize =200 Mpc^3)
2. Simulated Volume = 100 Mpc^3 (or 200 Mpc^3 for Number of lens = 11 )
3. nc = 128
4. field size = 5x5 deg^2 or (10x10 deg^2)
5. Convergence map resolution = 512 (or 1024 for 10x10 deg^2)
6. Lensplane resolution: 256

The specific setting can be found here
To follow, the result of 4 setting combinations compared to the Jax-cosmo linear power spectrum.

The two vertical lines indicate the scale l=300 and l=3000.

[dlanzieri]

I made the notebook run with different configurations.
What follows is part of the results of our tests.

1. Number of lens = 44 / 22 / 11  (according to the  simulated Volume)
2. Simulated Volume = 50 / 100 / 200  Mpc^3  
3. nc = 128           
4. field size = 5x5 deg^2 
5. Convergence map resolution = 512 
6. Lensplane resolution = 256

We were surprised to see how the change of the Box size from 100 to 200 Mpc^3 impacts the small scales, but how the small scales remain unchanged from 100 to 50 Mpc^3.
This can be seen in the matter power spectrum in the snapshots, we don't see any difference between the following plot (obtained with Box size=50 Mpc^3) and the one posted in the message above (Box size=100 Mpc^3)

We also expected a greater impact on the large scale, but we can see that the Box size affects only very large scale, larger than 300, out of range of "l" we are interested to.

1. Number of lens = 22
2. Simulated Volume = 100 Mpc^3  
3. nc = 128           
4. field size = 5x5 deg^2 
5. Convergence map resolution = 512 
6. Lensplane resolution = 256 / 512

As we can see, the lensplane resolution affect the angular power spectrum as well.
This is owning to the fact that an higher lensplane resolution has a lower smoothing effect, this causes an extra in power for the small scale but also a jump in the curve (caused by greater noise).

1. Number of lens = 22
2. Simulated Volume = 100 Mpc^3  
3. nc = 128           
4. field size = 5x5 deg^2 /  10x10 deg^2 /
5. Convergence map resolution = 512 / 1024
6. Lensplane resolution = 256 

As we can see, the field doesn't seem to have a particular impact on the angular power spectrum.

[dlanzieri]

After having seen how the change in the Box size impacts the power spectrum we decided to compute an additional test generating the snapshots by using a linear power spectrum at the scale factor of 0.2 .

The following results are computed with this setting :

1. Number of lens = 44
2. Simulated Volume = 50 Mpc^3
3. nc = 128
4. field size = 5x5 deg^2
5. Convergence map resolution = 512
6. Lensplane resolution = 128 / 256
   
   

As we can see, with a lensplane resolution = 128 we can reach enough power to match the theoretical power spectrum without introduce more noise.

[EiffL]

number of lens 22? for 50 Mpc box? Also, do you mean scale factor of 0.2?

[dlanzieri]

@EiffL sorry! I've just corrected, I used 44 lens and scale factor of 0.2

[dlanzieri]

I implemented this new test running the N-body simulation with the following setting:

box_size=50.    
nc = 128             
nsteps=40

The following image shows a comparison between the Jax-cosmo non linear power spectrum and the 3D Power spectrum computed for each snapshot.
Each snapshot at a specific scale factor is created twice, by two different values of the force resolution factor (B).

The plots are sorted in order of increasing value of the scale factor.