  The Cosmological Problem is considered in a five-dimensional (bulk) manifold
with two time coordinates, obeying vacuum Einstein field equations. 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 find
out the general solution, which happens to consist in a single metric. All the
embedded Friedmann-Robertson-Walker (FRW) metrics can be obtained from this
'mother' metric ('M-metric') in the bulk, by projecting onto different
four-dimensional hypersurfaces (branes). Having a time plane in the bulk allows
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). Explicit counter-examples are
provided, showing that not every spatially-flat FRW metric can actually be
embedded in a 3+2 bulk manifold. This implies that the extension of the
Campbell theorem to the General Relativity case works only in its weaker form
in this case, requiring as an extra assumption that the constraint equations
hold at least in a single 4D hypersurface.
