Artefacts in benchmark Cls

[tilmantroester]

This is to discuss some potential artefacts in the benchmark Cls. This applies to the clustering auto-correlations, especially at high redshift.

1. At large ell (~ell>1000), the benchmark Cls don't seem to agree with the Limber approximation:
   
   This is Cl_gg 9-9; in blue: CCL Limber; orange: independent non-Limber/Limber implementation by @rreischke.
   In this case, the region of ell > 1000 contributes ~25% to the SNR, so can't just be ignored.

2. ell = 2 looks weird:
   
   Again Cl_gg, 9-9. The ell = 2 mode contributes about 40% to the SNR.

[rreischke]

For completeness: I implemented my own "brute force" calculation, based on adaptive integration and this is what I get, again for Cl_gg, 9-9. Might be confirmation bias though.

[c-d-leonard]

@damonge and I (mostly @damonge!) are working on figuring this out, but to allow time for this to be properly understood, we are extending the final challenge deadline to February 5th! (see announcement at the top of the readme)

[damonge]

Update on this: the ell=2 artifact was caused by CCL ignoring the contribution from redshifts where the dN/dz was smaller than 0.001 of its maximum. This is alright for Limber, but not a good idea for non-Limber.

Still looking at the high-ell issue, but no luck so far. Will update benchmarks asap

[damonge]

@tilmantroester and all. I've posted new benchmarks in #22 . These fix the problem at ell=2 and now contain shear-shear power spectra with non-Limber at all ells (the previous ones used limber after ell=100).

I'm still investigating if there are problems above ell=1000. I haven't found any evidence for it, but I'm still running a few more checks.

[damonge]

Thanks to @c-d-leonard you can find these in master now.