Machine-learning cosmology from void properties

Cosmic voids are the largest and most underdense structures in the Universe. Their properties have been shown to encode precious information about the laws and constituents of the Universe. We show that machine learning techniques can unlock the information in void features for cosmological parameter inference. We rely on thousands of void catalogs from the GIGANTES dataset, where every catalog contains an average of 11,000 voids from a volume of $1~(h^{-1}{\rm Gpc})^3$. We focus on three properties of cosmic voids: ellipticity, density contrast, and radius. We train 1) fully connected neural networks on histograms from individual void properties and 2) deep sets from void catalogs, to perform likelihood-free inference on the value of cosmological parameters. We find that our best models are able to constrain the value of $\Omega_{\rm m}$, $\sigma_8$, and $n_s$ with mean relative errors of $10\%$, $4\%$, and $3\%$, respectively, without using any spatial information from the void catalogs. Our results provide an illustration for the use of machine learning to constrain cosmology with voids.