Volume averaging in the quasispherical Szekeres model

Abstract

This paper considers volume averaging in the quasispherical Szekeres model. The volume averaging became of considerable interest after it was shown that the volume acceleration calculated within the averaging framework can be positive even when the local expansion rate decelerates. This issue was intensively studied within spherically symmetric models. However, since our Universe is not spherically symmetric similar analysis is needed in non-symmetrical models. This papers presents the averaging analysis within the quasispherical Szekeres model which is a non-symmetrical generalisation of the spherically symmetric Lemaître–Tolman family of models. In the quasispherical Szekeres model the distribution of mass over a surface of constant t and r has the form of a mass-dipole superposed on a monopole. This paper shows that when calculating the volume acceleration, ä, within the Szekeres model, the dipole does not contribute to the final result, hence ä only depends on a monopole configuration. Thus, the volume averaging within the Szekeres model leads to literally the same solutions as those obtained within the Lemaître–Tolman model.