  In this work we derive a scenario {in which} the early universe consists of
{radiation fluid} and Bose-Einstein condensate. The possibility of
gravitational self-interaction due to an attractive Bose-Einstein condensate is
analyzed. The classical behavior of the scale factor of the universe is
determined by a parameter associated with the Bose-Einstein fluid with bouncing
or Big Crunch solutions. After we proceed to compute the finite-norm wave
packet solutions to the Wheeler-DeWitt equation. The behavior of the scale
factor is studied by applying the many-worlds interpretation of quantum
mechanics. The quantum cosmological model is free from the singularities.
