On Topological Modifications of Newton's Law
  Recent cosmological data for very large distances challenge the validity of
the standard cosmological model. Motivated by the observed spatial flatness the
accelerating expansion and the various anisotropies with preferred axes in the
universe we examine the consequences of the simple hypothesis that the
three-dimensional space has a global R^2 X S^1 topology. We take the radius of
the compactification to be the observed cosmological scale beyond which the
accelerated expansion starts. We derive the induced corrections to the Newton's
gravitational potential and we find that for distances smaller than the
S^1-radius the leading 1/r-term is corrected by convergent power series of
multipole form in the polar angle making explicit the induced anisotropy by the
compactified third dimension. On the other hand, for distances larger than the
compactification scale the asymptotic behavior of the potential exhibits a
logarithmic dependence with exponentially small corrections. The change of
Newton's force from 1/r^2 to 1/r behavior implies a weakening of the
deceleration for the expanding universe. Such topologies can also be created
locally by standard Newtonian axially symmetric mass distributions with
periodicity along the symmetry axis. In such cases we can use our results to
obtain measurable modifications of Newtonian orbits for small distances and
flat rotation spectra, for large distances at the galactic level.
