Publikace ÚTF

We study the behaviour of the density contrast in quasi-spherical Szekeres
spacetime and derive its analytical behaviour as a function of t and r . We set up the
inhomogeneity using initial data in the form of one extreme value of the density and
the radial profile. We derive conditions for density extremes that are necessary for
avoiding the shell crossing singularity and show that in the special case of a trivial
curvature function, the conditions are preserved by evolution.We also show that in this
special case if the initial inhomogeneity is small, the time evolution does not influence
the density contrast, however its magnitude homogeneously decreases.
Keywords Inhomogeneous cosmology · Szekeres spacetime · Shell crossing