Self-similar cosmologies in 5D: Our universe as a topological separation from an empty 5D Minkowski space

In this paper we find the most general self-similar, homogeneous and isotropic, Ricci flat cosmologies in 5D. These cosmologies show a number of interesting features: (i) the field equations allow a complete integration in terms of one arbitrary function of the similarity variable, and a free parameter; (ii) the three-dimensional spatial surfaces are flat; (iii) the extra dimension is spacelike; (iv) the general solution is Riemann-flat in 5D but curved in 4D, which means that an observer confined to 4D spacetime can relate this curvature to the presence of matter, as determined by the Einstein equations in 4D. We show that these cosmologies can be interpreted, or used, as 5D Riemann-flat embeddings for spatially-flat FRW cosmologies in 4D. In this interpretation our universe arises as a topological separation from an empty 5D Minkowski space, as envisioned by Zeldovich.