  In a Bohmian quantum cosmology scenario, we investigate some quantum effects
on the evolution of the primordial universe arising from the adoption of an
alternative non-trivial ordering to the quantization of the constrained
Hamiltonian of a minimally coupled scalar field. The Wheeler-DeWitt equation
has a contribution from the change in factor ordering, hence there are new
quantum effects. We compare the results between the non-trivial and the trivial
ordering cases, showing that the classical limit is valid for both orderings,
but new bouncing and cyclic solutions are present in the non-trivial case.
Additionally, we show that the non-singular solutions already present in the
trivial ordering formalism keep valid.
