Two families of cosmological solutions are presented in D = 6, N = 2 Kaluza-Klein supergravity theories. One family, which applies to the case that the universe is in a vacuum state, includes the (Minkowski space-time)×(constant sphere S2) solution. The case with four-dimensional radiation comprises the other family, which contains the (Friedmann universe)× (constant sphere S2) solution. All solutions in the latter family approach the Friedmann universe asymptotically. The four-dimensional cosmological constant vanishes automatically without fine-tuning in both families of solutions.
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