Add comoving volume element calculation to the background module

[tmcclintock]

An essential quantity to calculate is the comoving volume element, dV/dOmega dz, or the comoving volume per unit redshift and solid angle. This can be accomplished by combining splines already present in CCL. For reference, see eq. 28 of this paper by David Hogg.

The equation to be implemented is

This issue is very easy, and could serve as a good hack day project at CMU.

[c-d-leonard]

@tmcclintock I'm guessing you'd still like to see this?

[nikosarcevic]

Hi @nikfilippas ,

if you want, feel free to use the code for the coming volume that was coded by me, Marco Bonici and Matthijs van der Wild.
I also have a similar code in my own pipeline (a DESC Project).

Here is the link to the coming volume function in our code for CosmOracle https://github.com/nikosarcevic/CosmOracle/blob/main/background.py

Let me know if you need help with implementing it.

[nikfilippas]

Hey Niko! I have already implemented it in a Python-only version of CCL which I'll submit for review in a few weeks (hopefully), after some of the other stuff gets pushed to the main branch. It is here, but for now it only lives in my own repo. It isn't a much requested feature and that's why I have refrained from opening a separate PR just for this, so that the PR list isn't cluttered.
Having a quick look I think our implementations are equivalent, right?

[nikosarcevic]

Hey Niko! I have already implemented it in a Python-only version of CCL which I'll submit for review in a few weeks (hopefully), after some of the other stuff gets pushed to the main branch. It is here, but for now it only lives in my own repo. It isn't a much requested feature and that's why I have refrained from opening a separate PR just for this, so that the PR list isn't cluttered.
Having a quick look I think our implementations are equivalent, right?

I see! the only thing I would point out which is important is the omega_k part -- there is a good discussion around omega_k and David Hogg got good comments about it from Phillip Helbig back in the day. so we included that special case so have a look at our code, https://github.com/nikosarcevic/CosmOracle/blob/7dfdc63a127b7282dbbfa19db7b97789a611faca/background.py#L136

[nikfilippas]

Brief follow-up after discussion in private: CCL defines Cosmology objects given Ω_k, and then calculates Ω_Λ, while CosmOracle calculates Ω_k from a given Ω_Λ. Which essentially means that CCL doesn't suffer from this truncation problem.

[nikosarcevic]

indeed. thanks for making sure we clarified it here :)