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

TL;DR

This paper investigates the distance-redshift relation in a spherically symmetric inhomogeneous universe model with dust shells, finding it aligns with FL models under certain averaging conditions, supporting the universe's large-scale homogeneity.

Contribution

It demonstrates that an inhomogeneous dust-shell universe can replicate FL model relations when averaged, supporting the large-scale homogeneity hypothesis.

Findings

Distance-redshift relation matches FL models with homogeneous averaging.

Large inhomogeneities do not affect the overall relation when averaged.

Supports the idea that the universe appears homogeneous on large scales.

Abstract

The relation between angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. This model has large inhomogeneities of matter distribution on small scales. 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.