The behavior of perturbations is studied in cosmological models which consist of two different homogeneous regions connected in a spherical shell boundary. The junction conditions for the metric perturbations and the displacements of the shell boundary are analyzed and the surface densities of the perturbed energy and momentum in the shell are derived, using Mukohyama’s gauge-invariant formalism and the Israel discontinuity condition. In both homogeneous regions, the perturbations of scalar, vector, and tensor types are expanded using the three-dimensional harmonic functions, but the mode coupling among them is caused in the shell by the inhomogeneity. By treating the perturbations with odd and even parities separately, it is found, however, that we can have consistent displacements and surface densities for given metric perturbations.

• Received 18 August 2004

DOI:https://doi.org/10.1103/PhysRevD.70.123502