I began thinking about the problem I describe below from trying to understand the discussions in another thread. https://www.physicsforums.com/threads/concordance-cosmology-paper.909603This problem is about the expansion behavior of a “simple” universe model that might demonstrate a distinction between an expansion based on the average mass density, and an expansion based on a distribution of mass which is mostly vacuum. I start with a finite vacuum universe with five point masses equidistant form each other (a 4-simplex), and each having a fixed position with respect to a co-moving coordinate system. This universe being finite, it is closed with a positive curvature ~1/R(t) at places far from a point mass. The approximate volume of the universe is then V(t) ~= 2 π2 R(t)3. If each point mass as mass M, then the density ρ(t) ~= 5M/V(t).(The reason this is not exact is that the point masses distort the space and therefore the total volume. If this mass density were instead uniformly distributed, then the Friedmann Equation see https://en.wikipedia.org/wiki/Friedmann_equationscould be used to calculate the Hubble “constant” value H(t), and then numerically R(t). The problem is to calculate an estimate for the difference between the uniform density Friedmann solution, and a solution which is based on the five point masses.