Simulation based inference of the ionization history from the 2D 21 cm power spectrum

The 21 cm signal contains a wealth of information about the formation of the first stars and the reionization of the intergalactic medium during the Cosmic Dawn (CD) and Epoch of Reionization (EoR). The timing of these important milestones has only roughly been constrained through indirect measurements, such as from the cosmic microwave background (CMB) optical depth, and Lyman-$α$ forest. Therefore, inferring the neutral fraction over cosmic time is a goal of upcoming 21 cm experiments, such as the Square Kilometer Array (SKA). We contrast two approaches to infer astrophysical parameters and ionization history from 21 cm 2D power spectra (2DPS). We develop an emulator of the 21 cm 2DPS, trained on 21cmFAST simulations, taking into account the expected instrumental noise from the SKA and sample variance. We then perform simulation based inference (SBI) using neural posterior estimation (NPE). We compare training on datasets of noisy 2DPS obtained from 21cmFAST simulations and an emulator, to infer astrophysical parameters of interest. Using an emulator of the ionization history, which has been trained on simulations from the same astrophysical parameters, we then obtain posterior distributions of the ionization history over the redshift range z $\sim$ 5-12. We demonstrate that both methods are capable of accurately recovering the ionization history and astrophysical parameters. However, coverage tests indicate that adding emulated samples does not improve predictions. This work suggests that due to the stochastic nature of the 2DPS, using an emulator of this summary statistic may result in poorer inference.