Boltzmann Codes

Boltzmann Codes is the codes that numerically solving the background and the first-order Boltzmann equations of all matters in our universe. It's can be used to calculate observables, i.e., the power spectrum of fluctuations of matters.

There are various mature codes for these calculations, such as CAMB, CLASS et.al and their extensions. Writing your own Boltzmann Codes is not only for teaching purposes, but also for effectively modify the codes according to your own needs. This is important today as we need to consider something more than standard cosmology.

I here provide a brief introduction and clarify some tricks for these calculations. We should finally obtaion plots of observables, like the matter or the CMB power spectrums. The codes, written in Mathematica, can be found in my homepage CMBsnail. However, I strongly suggest you to code your own one. More details can be found in some advanced papers^[1,2] and a wonderful course of CMB calculations: Cosmology II.

This Boltzmann Codes is divided into these four parts:

   Background: solving the background evolution of all matters during the Hot Bing Bang universe.

   Recombination: solving the history of decoupling between photons and baryons.

   Perturbation: solving the first-order evolution of all matters accroding to the background and recombination history.

   Power Spectrum: calculating the CMB power spectrum by using the Line-of-Sight integtation.

We also calculate the axion dark matter(DM):

   Axion DM: Introducing axion as dark matter and solving its background and first-order evolution under effective fluid treatments^[3].

Splines

[1] C. P. Ma and E. Bertschinger, ``Cosmological perturbation theory in the synchronous and conformal Newtonian gauges,'' Astrophys. J. 455, 7-25 (1995) doi:10.1086/176550 [arXiv:astro-ph/9506072 [astro-ph]].
[2] P. Callin, ``How to calculate the CMB spectrum,'' [arXiv:astro-ph/0606683 [astro-ph]].
[3] S. Passaglia and W. Hu, ``Accurate effective fluid approximation for ultralight axions,'' Phys. Rev. D 105, no.12, 123529 (2022) doi:10.1103/PhysRevD.105.123529 [arXiv:2201.10238 [astro-ph.CO]].