Observations of the cosmic 21-cm power spectrum (PS) are starting to enable precision Bayesian inference of galaxy properties and physical cosmology, during the first billion years of our Universe. Here we investigate the impact of common approximations about the likelihood used in such inferences, including: (i) assuming a Gaussian functional form; (ii) estimating the mean from a single realization; and (iii) estimating the (co)variance at a single point in parameter space. We compare ‘classical’ inference that uses an explicit likelihood with simulation-based inference (SBI) that estimates the likelihood from a training set. Our forward models include: (i) realizations of the cosmic 21-cm signal computed with 21cmFAST by varying ultraviolet (UV) and X-ray galaxy parameters together with the initial conditions; (ii) realizations of the telescope noise corresponding to a $1000 \, \mathrm{h}$ integration with the low-frequency component of the Square Kilometre Array (SKA1-Low); and (iii) the excision of Fourier modes corresponding to a foreground-dominated horizon ‘wedge’. We find that the 1D PS likelihood is well described by a Gaussian accounting for covariances between wave modes and redshift bins (higher order correlations are small). However, common approaches of estimating the forward-modelled mean and (co)variance from a random realization or at a single point in parameter space result in biased and overconstrained posteriors. Our best results come from using SBI to fit a non-Gaussian likelihood with a Gaussian mixture neural density estimator. Such SBI can be performed with up to an order of magnitude fewer simulations than classical, explicit likelihood inference. Thus SBI provides accurate posteriors at a comparably low computational cost.
Preparing for a first detection of the 21-cm signal during reionization by large-scale interferometer experiments requires rigorous testing of the data analysis and reduction pipelines. Validating that these do not erroneously add/remove features mimicking the signal (e.g. from side lobes or large-scale power leakage) requires simulations extending beyond the primary field of view. However, the Murchison Wide Field Array (MWA) with a field of view of ∼252 deg2 would require simulations spanning several Gpcs, which are currently infeasible. To address this, we developed a simplified version of the seminumerical reionization simulation code 21cmfast, sacrificing some physical accuracy (linear structure formation) in favour of extremely large volumes. We then constructed a 7.5 Gpc comoving volume specifically tailored to the binned spectral resolution of the MWA (∼1.17 cMpc), required for validating the pipeline used in the 2020 MWA 21-cm power spectrum (PS) upper limits. With this large-volume simulation, we then explored: (i) whether smaller volume simulations are biased by missing large-scale modes, (ii) non-Gaussianity in the cosmic variance uncertainty, (iii) biases in the recovered 21-cm PS following foreground wedge avoidance, and (iv) the impact of tiling smaller simulations to achieve large volumes. We found (i) no biases from missing large-scale power, (ii) significant contribution from non-Gaussianity, as expected, (iii) a 10–20 per cent overestimate of the 21-cm PS following wedge mode excision, and (iv) tiling smaller simulations underestimates the large-scale power and cosmic variance.
more » « less- PAR ID:
- 10372498
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 516
- Issue:
- 4
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 5588-5600
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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