The Effect of Physical Assumptions on the Calculation of Microwave Background Anisotropies

As the data on CMB anisotropies improve and potential cosmological applications are realized, it will be increasingly important for theoretical calculations to be as accurate as possible. All modern calculations for inflationary-inspired fluctuations involve the numerical solution of coupled Boltzmann equations. There are many assumptions and choices to be made when carrying out such calculations. We go through each in turn, pointing out the best selections to make, and the level of inaccuracy expected through incorrect choice: (1) neglecting the effects of neutrinos or polarization has a 10% effect; (2) varying radiation temperature and He fraction can have smaller, but noticeable effects; (3) numerical issues, such as k-range and smoothing are discussed; (4) short-cut methods, e.g. free-streaming and tilt approximations, are generally inadequate at the few % level; (5) at the 1% level somewhat baroque effects are important, such as He recombination and even minimal reionization; (6) at smaller angular scales there are secondary effects which will ultimately have to be considered. Extracting information from the subsidiary acoustic peaks and the damping region will be an extremely challenging problem. However, given the prospect of measuring just such information on the sky, it will be important to meet this challenge. In principle we can obtain details about reionization history, neutrino contribution, helium abundance, non-power-law initial conditions etc.