Adds ODEs for structure growth. Makes WCDM and LCDM initialization more uniform.

[dforero0896]

Hi,
I have taken the liberty to add some functionality by providing a function to compute the growth factor and its first and second derivatives. So far I have not been able to redefine the Cosmology structures so that they allow for a cache in order to avoid re-solving the ODE in each call like fastpm does, for example. I have added tests for this part in the test suite.

I have also modified the Cosmology structures so they are all defined as the WCDM were, within the loop. I think this makes development much easier. Moreover, I made the structures able to accept kwargs instead and changed the relevant parameters for the definition of a cosmology. In particular, OmegaR, and OmegaM are now derived from OmegaC, OmegaB, Neff and T_cmb. Nonetheless, I have left OmegaM and OmegaR kewords in the cosmology function so the tests are still compatible.

Please feel free to check and modify as you please and merge if you find these modifications useful :). Also don;t hesitate to write back if there are any questions.
Thanks!

[codecov]

Codecov Report

❌ Patch coverage is 90.00000% with 7 lines in your changes missing coverage. Please review.
✅ Project coverage is 93.96%. Comparing base (04b978f) to head (0053248).

Files with missing lines	Patch %	Lines
src/Cosmology.jl	90.00%	7 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##              main      #45      +/-   ##
===========================================
- Coverage   100.00%   93.96%   -6.04%     
===========================================
  Files            1        1              
  Lines           78      116      +38     
===========================================
+ Hits            78      109      +31     
- Misses           0        7       +7     

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[marcobonici]

Is there any update on this PR?
I have implemented in some of my packages a growth factor evaluation using DiffEq, which looks quite similar to the written here. It would be nice to have a single, community tested implementation for this kind of calculation.

[giordano]

Sorry, I personally never had the time to look into this also because I'm not much into this field. However I'd note that DifferentialEquations.jl is a quite heavy dependency which I'd rather not add to such a lightweight package like Cosmology.jl. Is there any possibility of making this feature a package extension, so that it's enabled only if DifferentialEquations.jl is already present in the environment?

[abhro]

Now that SciML broke up its big packages into smaller components, depending on what's being used, could we change the dependency into OrdinaryDiffEq.jl or something?

[abhro]

Merge conflicts "technically" resolved if you squint, but I'll be making more commits soon to actually get the code correct

[abhro]

To limit the scope of this PR, I'm thinking if the re-definition of the structs should be removed and deferred for a later date, only keeping the ODE and new functions here.