  The Friedmann equation for a positive tension brane situated between two bulk
spacetimes that posses the same 5D cosmological constant, but which does not
posses a Z_2 symmetry of the metric itself is derived, and the possible effects
of dropping the Z_2 symmetry on the expansion of our Universe are examined;
cosmological constraints are discussed. The global solutions for the metric in
the infinite extra dimension case are found and comparison with the symmetric
case is made. We show that any brane world senario of this type must revert to
a Z_2 symmetric form at late times, and hence rule out certain proposed
scenarios.
