Average zero-expansion regions of the universe

Abstract

Persistent tensions in the $\Lambda$CDM cosmological model underline the importance of tests of its basic assumptions. One such potential test arises from the fact that the surface of zero expansion around the collapsing object with spherical symmetry is strictly related to the object's mass and the value of the cosmological constant. We propose a complementary probe relating the averaged zero-expansion volume to the mass and the background cosmological Hubble parameter. Using the relativistic Zel'dovich approximation we are able to relax the spherical symmetry assumption and hence obtain a more general test of cosmological dynamics. Alternatively, our method can serve as a test of compatibility of relativistic N-body simulations and the scalar, averaged Einstein's equations with the relativistic Zel'dovich approximation serving as a closure condition.