A semi-analytical approach to cosmic void evolution

We present a theoretical study of the non-linear evolution of cosmic voids -- underdense regions that occupy a large fraction of the observable Universe. We model a void as an isolated homogeneous spheroidal (axisymmetric) ellipsoid embedded in a homogeneous $\Lambda$CDM universe. Starting from a small initial density contrast at redshift $z=500$, we numerically integrate the equations of motion for the ellipsoid semi-axes and follow their evolution to the present epoch. We examine the anisotropic expansion of the void and the corresponding change in its shape, characterised by the eccentricity $e$. We find that the void non-sphericity always decreases, but rather slowly: the eccentricity drops from $e\approx0.87$ at $z=500$ to $e\approx0.81$ at $z=0$. Thus the void becomes rounder but remains aspherical throughout the evolution. The evolution and final value of the void underdensity are virtually independent of the void's eccentricity. The nonlinearity of void evolution becomes apparent very early: a ten percent deviation from the linear regime occurs already at $z\simeq8$, when $\varepsilon = \Delta\rho/\rho\sim10\%$. Notably, our calculations show that the majority of voids are not strongly underdense and contain a significant amount of matter, $\mu>0.5$.