Void Number Counts as a Cosmological Probe for the Large-Scale Structure

Void number counts (VNC) indicates the number of low-density regions in the large-scale structure (LSS) of the Universe, and we propose to use it as an effective cosmological probe. By generating the galaxy mock catalog based on Jiutian simulations and considering the spectroscopic survey strategy and instrumental design of the China Space Station Telescope (CSST), which can reach a magnitude limit $\sim$23 AB mag and spectral resolution $R\gtrsim200$ with a sky coverage 17,500 deg$^2$, we identify voids using the watershed algorithm without any assumption of void shape, and obtain the mock void catalog and data of the VNC in six redshift bins from $z=0.3$ to1.3. We use the Markov Chain Monte Carlo (MCMC) method to constrain the cosmological and VNC parameters. The void linear underdensity threshold $\delta_{\rm v}$ in the theoretical model is set to be a free parameter at a given redshift to fit the VNC data and explore its redshift evolution. We find that, the VNC can correctly derive the cosmological information, and the constraint strength on the cosmological parameters is comparable to that from the void size function (VSF) method, which can reach a few percentage levels in the CSST full spectroscopic survey. This is because that, since the VNC is not sensitive to void shape, the modified theoretical model can match the data better by integrating over void features, and more voids could be included in the VNC analysis by applying simpler selection criteria, which will improve the statistical significance. It indicates that the VNC can be an effective cosmological probe for exploring the LSS.