A point-particle model universe

The observable cosmos is modeled as a set of point-particles, representing the galaxies, which perturb a dust-filled, Robertson-Walker space-time. The analysis proceeds only to first order in k = 8πG/c2 and employs a metric suggested by McVittie, whose original work this paper seeks to develop. Necessary and sufficient conditions are found for the metric to give rise to an energy tensor of a chosen form appropriate to the modeling. In particular, a second-order equation is found which governs a certain time-independent potential. A class of solutions to this equation is established, and the associated singularities of the mass density are shown to be of a Dirac type. (author)