3+2 Cosmology: unifying FRW metrics in the bulk

The Cosmological Problem is considered in a five-dimensional (bulk) manifold with two time coordinates, where the vacuum Einstein field equations are enforced. The evolution formalism is used there, in order to get a simple form of the resulting constraints. In the spatially flat case, this approach allows to show that all Friedmann-Robertson-Walker (FRW) metrics can be obtained from a single metric in the bulk, by projecting onto different four-dimensional hypersurfaces (branes). This 'M-metric' is shown to be unique in the non-trivial case. Having a time plane in the bulk allows one to devise the specific curve which will be kept as the physical time coordinate in the brane. This method is applied for identifying FRW regular solutions, evolving from the infinite past (no Big Bang), even with an asymptotic initial state with non-zero radius (emergent universes).