Distance-redshift relation in an isotropic inhomogeneous universe II: Spherically symmetric dust-shell universe

TL;DR

This paper investigates how the distance-redshift relation in a spherically symmetric dust-shell universe aligns with Friedmann-Lemaitre models when averaged density and expansion laws are homogeneous, supporting the universe's large-scale homogeneity.

Contribution

It demonstrates that a spherically symmetric dust-shell universe's distance-redshift relation matches FL models under homogeneous averaging, supporting the large-scale homogeneity hypothesis.

Findings

Relation agrees with FL models under homogeneous averaging

Supports the averaging hypothesis for large-scale homogeneity

Discusses impact of local inhomogeneities on cosmological parameter estimation

Abstract

The relation between the angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre (FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales. We also study the connection of the proper mass of a shell with the mass of gravitationally bound objects. Combining this with the results of the distance-redshift relation, we discuss an impact of the local inhomogeneities on determination of the cosmological parameters through the observation of the locally inhomogeneous universe.