  A six-dimensional universe with two branes in the "football-shaped" geometry
leads to an almost realistic cosmology. We describe a family of exact solutions
with time dependent characteristic size of internal space. After a short
inflationary period the late cosmology is either of quintessence type or turns
to a radiation dominated Friedmann universe where the cosmological constant
appears as a free integration constant of the solution. The radiation dominated
universe with relativistic fermions is analyzed in detail, including its
dimensional reduction.
