$Λ$ effect in the cosmological expansion of voids

Abstract

The dynamical effect of the cosmological constant $Λ$ on a single spherical void evolving in a the universe is investigated within a non linear perturbation of Newton-Friedmann models. The void expands with a huge initial burst which freezes asymptotically with time up to matching Hubble flow. For $Ω_{\circ}\sim 0.3$, $Λ$-effect on the kinematics intervenes significantly by amplifying the expansion rate at redshift $z\sim 1.7$. As a result, the size increases with the background density and with $Λ$, what interprets by the gravitational attraction of borders from outside regions and the gravitational repulsion of borders. The velocity flow within the void region depends solely on $Λ$, it reads $\vec{v}=\sqrt{Λ/3}\vec{r}$. Hence, the empty regions are swept out for spatially closed Friedmann models what provides us with a stability criterion.