Generalized Swiss-Cheese Cosmologies II: Spherical Dust

TL;DR

This paper investigates whether evolving boundary surfaces can be incorporated into generalized Swiss-cheese cosmological models with dust, concluding that the boundary must remain exactly comoving to satisfy junction conditions, thus limiting realism.

Contribution

It demonstrates that in Swiss-cheese models with dust, boundary surfaces cannot evolve unless assumptions are relaxed, clarifying constraints on realistic inhomogeneous cosmologies.

Findings

Boundary must remain exactly comoving to satisfy junction conditions

Allowing boundary evolution requires dropping dust assumption or adding surface layers

Original model constraints are reinforced by junction condition analysis

Abstract

The generalized Swiss - cheese model, consisting of a Lema\^itre - Tolman (inhomogeneous dust) region matched, by way of a comoving boundary surface, onto a Robertson-Walker background of homogeneous dust, has become a standard construction in modern cosmology. Here we ask if this construction can be made more realistic by introducing some evolution of the boundary surface. The answer we find is no. To maintain a boundary surface using the Darmois - Israel junction conditions, as opposed to the introduction of a surface layer, the boundary must remain exactly comoving. The options are to drop the assumption of dust or allow the development of surface layers. Either option fundamentally changes the original construction.