An Alcock-Paczynski Test on Reionization Bubbles for Cosmology

In this paper, we propose an Alcock-Paczy\'nski (AP) test to constrain cosmology using HII bubbles during the Epoch of Reionization. Similarly to cosmic voids, a stack of HII bubbles is spherically symmetric because ionizing fronts propagate isotropically on average (even if individual bubbles may not be spherical), making them standard spheres to be used in an AP test. Upcoming 21-cm observations, from the Square Kilometer Array (SKA) for instance, will contain tomographic information about HII regions during reionization. However, extracting the bubbles from this signal is made difficult because of instrumental noise and foreground systematics. Here, we use a neural network to reconstruct neutral-fraction boxes from the noisy 21-cm signal, from which we extract bubbles using a watershed algorithm. We then run the purely geometrical AP test on these stacks, showing that a SKA-like experiment will be able to constrain the product of the angular-diameter distance $D_{\text{A}}$ and Hubble parameter $H$ at reionization redshifts with $\sim 2\%$ precision, robustly to astrophysical and cosmological uncertainties within the models tested here. This AP test, whether performed on 21-cm observations or other large surveys of ionized bubbles, will allow us to fill the knowledge gap about the expansion rate of our Universe at reionization redshifts.