Reduced multilevel atom method for calculating cosmological recombination kinetics

Abstract

A new method for solving the differential-algebraic set of equations, describing the kinetics of primary plasma recombination in the early Universe, is proposed. The method is based on the use of some properties of the initial high-dimensional set to construct a low-dimensional set which is mathematically equivalent in essentiality to the initial set. At the expense of certain complication of the algorithm for computing the coefficients describing the model atom with a small number of bound states, in comparison with conventional methods, complete agreement between the solution to the obtained low-dimensional set and corresponding components of the initial set is achieved. The described method allows construction of the algorithm for solving the recombination kinetics whose accuracy is comparable to integration of the complete multilevel set of kinetic equations and whose computational burden per model is comparable to the method used in the RECFAST code.