Apparent numerical instability of delta_cdm at very high k

[davidcato]

Hi all,

I'm trying to use CLASS to follow the evolution of delta_cdm at very high k and I have stumbled into a weird issue.

Basically, for k=5e3, I found that setting start_large_k_at_tau_h_over_tau_k = 0.007 and curvature_ini = 1.00001, leads to a 35% of the value of delta_cdm today compared to the default setting start_large_k_at_tau_h_over_tau_k = 0.05 and curvature_ini = 1. This 35% change is inconsistent with the subtle change in the initial conditions. See figure below:

Playing around I noticed that this spurious and inconsistent enhancement of delta_cdm is presented, although with different magnitudes, for basically any value of start_large_k_at_tau_h_over_tau_k < 0.05. When using the default value, I get at a 1e-5 change in delta_cdm consistent with curvature_ini = 1.00001, see figure below:

It looks like this funny behavior starts around the TCA (see the vertical dashed lines in the plots), but I do not have an intuition of why changing start_large_k_at_tau_h_over_tau_k will mess up with the TCA approximation. I'm using CLASS v3.2.0 (although I've found the same problem with v2.6.3) and in both cases I've set P_k_max_h/Mpc = 1e4. I've found similar results for k=5e2.

Do you have an idea of what would causing this issue? Perhaps I need to tune other precision params?

Thanks in advance!

Best,
David