The optical depth to reionization, a key parameter in the standard $\mathrm{\Lambda }\mathrm{CDM}$ cosmological model—which describes the Universe using six parameters and includes a cosmological constant ($\mathrm{\Lambda }$) and cold dark matter (CDM)—can be computed within astrophysical frameworks for star formation by modeling the evolution of the intergalactic medium. Accurate evaluation of this parameter is thus crucial for joint statistical analyses of cosmic microwave background (CMB) data and late-time probes such as the 21 cm power spectrum, requiring consistent integration into cosmological solvers. However, modeling the optical depth with sufficient precision in a computationally feasible manner for Markov chain Monte Carlo (MCMC) analyses is challenging due to the complexities of the nonlinear astrophysics. We introduce Neural Network Emulator for Reionization and Optical depth (nnero), a framework that leverages neural networks to emulate the evolution of the free-electron fraction during cosmic dawn and reionization. We demonstrate its effectiveness by simultaneously constraining cosmological and astrophysical parameters in both standard cold dark matter and noncold dark matter scenarios, including models with massive neutrinos and warm dark matter, showcasing its potential for efficient and accurate parameter inference.

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• Cosmological parameters
• Dark matter
• Evolution of the Universe
• Machine learning