Void spin distribution as a powerful probe of $\sigma_{8}$

We present a numerical proof of the concept that the void spin distributions can provide a tight constraint on the amplitude of matter density fluctuation on the scale of $8\,h^{-1}{\rm Mpc}$ ($\sigma_{8}$) without being severely deteriorated by the degeneracies of $\sigma_{8}$ with cold dark matter density parameter multiplied by the dimensionless Hubble parameter square ($\Omega_{\rm cdm}h^{2}$), total neutrino mass ($M_{\nu}$) and dark energy equation of state ($w$). Applying the Void-Finder algorithm~\cite{HV02} to a total of $15$ AbacusSummit $N$-body simulations of $15$ different cosmological models~\cite{summit1}, we identify the giant voids and measure the magnitudes of rescaled specific angular momenta of point-like void halos as their spins. The $15$ cosmologies include the Planck $\Lambda$CDM and $14$ non-Planck models, each of which differs among one another only in one of $\{\sigma_{8},\ \Omega_{\rm cdm}h^{2},\ M_{\nu},\ w\}$. We determine the probability density distribution of void spins for each model and for the first time find it to be well approximated by the generalized Gamma distribution with two characteristic parameters, $k$ and $\theta$. It turns out that the best-fit values of $k$ and $\theta$ exhibit very sensitive dependence only on $\sigma_{8}$, being almost insensitive to $\Omega_{\rm cdm}h^{2}$, $M_{\nu}$ and $w$. This exclusive $\sigma_{8}$-dependence of the void spin distributions is confirmed to be robust against the variation of the mass and number cuts of void halos. We also test an observational feasibility of estimating the void spins from real data on the galaxy redshifts.