Some Basic Questions

[lawrennd]

Which are the fundamental parameters of the CMB? Are they these here:

pars.set_cosmology(H0=67.5, ombh2=0.022, omch2=0.122, mnu=0.06, omk=0, tau=0.06)

Am I right to try and decompose into how much mass/energy, dark matter and dark energy these are?

Do we expect these to be the final set of parameters underlying the CMB and other parameters are due to effects such as gravitational lensing etc? Or am I missing something here.

[ixkael]

Yes, the fundamental parameters of the CMB are the energy densities of the various constituents of the universe, plus a couple of parameters for the initial conditions and the optical depth. In the standard cosmological model (flat LCDM with inflationary initial conditions, which is still highly favored by all data sets) those six parameters entirely determine the power spectrum of the CMB (and that it is a Gaussian random field).

In detail, this calculation is fairly complicated and does indeed involve various effects like gravitational lensing. But those are still described by those parameters: the amount of lensing is fixed by the energy densities and affects the CMB in a deterministic way, so there are no extra random variables. For example, the CAMB code does produce both the lensed and unlensed CMB power spectrum. When simulating maps of both CMB temperature and polarization (which I haven't described them in any notebooks, but I will), there are standard procedure for self-consistently generating lensed power spectra and simulating correlated maps with all those effects.

Alternative cosmological models have extra parameters, but this typically adds them to $\theta$. Viable models don't add new sources of stochasticity or drastically change the way the CMB power spectrum is calculated. For instance, exotic modified gravity or dark matter or energy models will involve extra parameters which will simply affect the CMB power spectrum and the statistics of the galaxy distribution. In fact, most cosmological models are nested.

Let me know if anything is unclear and I can send more concrete descriptions with pointers to the literature.