I have a question regarding the Coulomb interaction in spaces with non-trivial topology. Suppose we have D large spatial dimensions (D>2). Then the Coulomb potential is VC(r) ~ 1/rD-2. Usually one shows in three dimensions that the Coulomb potential VC(r) is nothing else but the Fourier transform of G(k) ~ 1/k² which is a Greens function for a massless particle; with a mass-term there would be an additional factor exp-mr. Now suppose that we do not have flat space but that space is compactified. The simplest example is a 3-torus with size L. Then one charge located at r=0 "feels" another charge located at r as if it were located at r, r + Lei, r + 2Lei, ... this is equivalent to say that the potential must be periodic on the 3-torus, i.e. it must respect the condition V(r) = V(r + Lei) One can discretize the theory by using Fourier modes on the 3-torus T3 = S1 * S1 * S1. Then the Coulomb potential V(r) can be derived from G(k) via a discrete Fourier series where one sums over 1/k² where k respects the periodicity of the 3-torus. So far so good. What happens if 1) the topology of space (spacetime) becomes more complex? There are e.g. speculations that our universe could have the topology of a dodecahedral space which could explain suppressions of CMB multipole moments. 2) the geometry of space becomes dynamic? In GR the geometry of space is not fixed; typically space(time) will expand. I have no idea how a mode decomposition in a dodecahedral space would look like. I have no idea how this could affect the Coulomb interaction at early times (for a small universe). I have no idea how the topology of an expanding universe would restrict the mode decomposition. Are there any hints how all this could affect such a simple law as the Coulomb interaction?