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Christopher M. Hirata developed the HyRec calculation of cosmological recombination with Yacine Ali-Haïmoud. Their method couples atomic level populations, the free electron fraction and radiative transfer, including two-photon transitions and diffusion near the Lyman-alpha line.^[ref]

The scientific need is predictive accuracy: the free electron population sets the Thomson scattering history that shapes Cosmic microwave background anisotropy. Equilibrium ionization alone cannot capture the entire decoupling process.

Yacine Ali-Haïmoud, with Christopher M. Hirata, produced the HyRec model of primordial hydrogen and helium recombination. It combines an effective multilevel-atom treatment with detailed photon transport while exploiting the sparse coupling structure to make repeated cosmological calculations practical.^[ref]

This connects atomic transition rates to cosmological inference: a changed recombination history changes the probability that a cosmic microwave background photon scatters before reaching the observer.