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

Norimasa Sugiura·Ken-ichi Nakao·Tomohiro Harada
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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.

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Norimasa Sugiura, Ken-ichi Nakao, Tomohiro Harada. 1999-11-24. Distance-redshift relation in an isotropic inhomogeneous universe II: Spherically symmetric dust-shell universe. https://doi.org/10.1103/physrevd.60.103508

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