Effective conductance method for the primordial recombination spectrum

TL;DR

This paper introduces a fast, efficient method for calculating the primordial recombination spectrum by factoring emissivity into cosmology-independent and dependent parts, significantly reducing computational time.

Contribution

The authors develop a conductance-based factorization approach that accelerates recombination spectrum calculations by over four orders of magnitude compared to traditional methods.

Findings

Recombination spectrum computation time reduced to less than a second

Method accurately computes helium and hydrogen recombination spectra

Fast code for primordial spectrum will be publicly available

Abstract

As atoms formed for the first time during primordial recombination, they emitted bound-bound and free-bound radiation leading to spectral distortions to the cosmic microwave background. These distortions might become observable in the future with high-sensitivity spectrometers, and provide a new window into physical conditions in the early universe. The standard multilevel atom method habitually used to compute the recombination spectrum is computationally expensive, impeding a detailed quantitative exploration of the information contained in spectral distortions thus far. In this work it is shown that the emissivity in optically thin allowed transitions can be factored into a computationally expensive but cosmology-independent part and a computationally cheap, cosmology-dependent part. The slow part of the computation consists in pre-computing temperature-dependent effective "conductances", linearly relating line or continuum intensity to departures from Saha equilibrium of the lowest-order excited states (2s and 2p), that can be seen as "voltages". The computation of these departures from equilibrium as a function of redshift is itself very fast, thanks to the effective multilevel atom method introduced in an earlier work. With this factorization, the recurring cost of a single computation of the recombination spectrum is only a fraction of a second on a standard laptop, more than four orders of magnitude shorter than standard computations. The spectrum from helium recombination can be efficiently computed in an identical way, and a fast code computing the full primordial recombination spectrum with this method will be made publicly available soon.