On the solution of the Kompaneets equation in cosmological context: a numerical code to predict the CMB spectrum under general conditions

Interpretation of current and future data calls for a continuous improvement in the theoretical modeling of CMB spectrum. We describe the new version of a numerical code, KYPRIX, specifically written to solve the Kompaneets equation in a cosmological context under general assumptions. We report on the equation formalism, and structure and computational aspects of the code. New physical options have been introduced in the current code version: the cosmological constant in the terms controlling the general expansion of the Universe, the relevant chemical abundances, and the ionization history, from recombination to cosmological reionization. We present some of fundamental tests we carried out to verify the accuracy, reliability, and performance of the code. All the tests demonstrate the reliability and versatility of the new code version and its accuracy and applicability to the scientific analysis of current CMB spectrum data and of much more precise measurements that will be available in the future.