CRRfast: an emulator for the cosmological recombination radiation with effects from inhomogeneous recombination

Abstract

ABSTRACT The cosmological recombination radiation (CRR) is one of the guaranteed ΛCDM spectral distortion (SD) signals. Even if very small in amplitude, it provides a direct probe of the three recombination eras, opening the path for testing one of the key pillars in our cosmological interpretation of the measured CMB anisotropies. Here, we develop a new emulator, CRRfast, to quickly and accurately represent the CRR for a wide range of cosmologies, using the state-of-the-art CosmoSpec code as a reference. CRRfast has been made publicly available both as stand-alone code and as part of class, thereby completing the set of average ΛCDM sources of SDs that can be modelled with class. With this newly developed pipeline we investigate the full constraining power of SDs within ΛCDM and highlight possible future applications to experimental design optimization. Furthermore, we show that the inhomogeneous evolution of the recombination process imprints second-order contributions to the CRR spectrum, leading to a broadening and shifting of the CRR features. These second-order terms are naturally captured by the emulator and allow us to evaluate the contribution of the ΛCDM primordial perturbations to the average CRR as well as to illustrate the effect of perturbed recombination due to Primordial Magnetic Fields (PMFs). As it turns out, while the second-order ΛCDM signal can be neglected, it could be significantly enhanced in the beyond-ΛCDM models. In particular in the case of PMFs, we demonstrate that through these non-linear terms the parameter space relevant to the Hubble tension could be tested with future CMB spectrometers.