Five Dimensional bigravity. New topological description of the Universe
  We extend the bimetric description of the Universe to a five-dimensional framework. Starting from Souriau's work (1964) we use two Robertson-Walker metrics with an extra term corresponding to the additional Kaluza fifth dimension. This first order model is limited to zero electric charge and electromagnetic energy densities. Assuming the massive particles, with positive or negative mass and energies owing finite lifetimes, it restores the O(3) symmetry and makes the generalized gauge process to restart. As a consequence the speed of light tends to zero. We assume the Universe to be closed over all its dimensions. Then, following an idea introduced in 1994 we describe the Universe as the two folds cover of a projective space. The arrow of time, mass and energy inversions arise as consequences of this geometrical hypothesis and fits the bimetric model. We choose to eliminate the "initial singularity", replaced by a boundary space, which is found to be euclidean. 
Jean Pierre Petit, Gilles d'Agostini