Volume averaging in the quasispherical Szekeres model

TL;DR

This paper investigates volume averaging in the non-symmetrical quasispherical Szekeres model, showing that the dipole component does not affect volume acceleration, resulting in solutions similar to the spherically symmetric Lemaître--Tolman model.

Contribution

It extends volume averaging analysis to the non-symmetrical Szekeres model, demonstrating the dipole's non-contribution to volume acceleration.

Findings

Dipole does not influence volume acceleration in the Szekeres model.

Volume averaging results match those of the Lemaître--Tolman model.

Volume acceleration can be positive despite local deceleration.

Abstract

This paper considers the 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 though the local expansion rate is always decelerating. 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 Lema\^itre--Tolman family of models. Density distribution in the quasispherical Szekeres has a structure of a time-dependent mass dipole superposed on a monopole. This paper shows that when calculating the volume acceleration, $\ddot{a}$, within the Szekeres model, the dipole does not contribute to the final result, hence $\ddot{a}$ only depends on a monopole configuration. Thus, the volume averaging within the Szekeres model leads to literally the same solutions as obtained within the Lema\^itre--Tolman model.