Is a Topology Change After a Big Rip Possible?

Understand

Motivated by condensed matter physical systems, in which a finite-time singularity indicates that the topology of the system changes, we critically examine the possibility of the Universe's topology change at a finite-time cosmological singularity.

• We emphasize on Big Rip and Type II and IV cosmological singularities, which we classify to future spacelike and timelike singularities.
• For the Type IV and Type II singularities, since no geodesics incompleteness occurs, no topological change is allowed, by using Geroch's theorem arguments.
• However, for the Big Rip case, Tipler's arguments allow a topology change, if the spacetime in which the topology change occurs is non-compact and the boundary of this region are two topologically distinct three dimensional spacelike partial Cauchy hypersurfaces.