Prior to recombination photons, electrons, and atomic nuclei rapidly scattered and behaved, almost, like a single tightly-coupled photon-baryon plasma. In order to solve the cosmological perturbation equations during that time, Cosmic Microwave Background (CMB) codes use the so-called tight-coupling approximation in which the problematic terms (i.e. the source of the stiffness) are expanded in inverse powers of the Thomson Opacity. Most codes only keep the terms linear in the inverse Thomson Opacity. We have developed a second-order tight-coupling code to test the validity of the usual first-order tight-coupling code. It is based on the publicly available code CAMB.

The sterile neutrino production code sterile-dm incorporates new elements to the calculations of the neutrino opacity at temperatures 10 MeV ≤ T ≤ 10 GeV and folds the asymmetry redistribution and opacity calculations into the sterile neutrino production computation, providing updated PSDs for the range of parameters relevant to the X-ray excess. The code requires several data files, which are included. With each run, sterile-dm creates a new output sub-directory that contains a parameter file listing the mass, mixing angle, initial lepton asymmetry and other information, a state file, which includes, among other states, the temperature and FRW coordinate time, and a set of snapshot files, one for each line in the state file.