  We study the quantum avoidance of the big rip singularity in the
Eddington-inspired-Born-Infeld (EiBI) phantom model. Instead of considering a
simple phantom dark energy component, which is described by a perfect fluid, we
consider a more fundamental degree of freedom corresponding to a phantom scalar
field with its corresponding potential, which would lead the classical universe
to a big rip singularity. We apply a quantum geometrodynamical approach by
performing an appropriate Hamiltonian study including an analysis of the
constraints of the system. We then derive the Wheeler-DeWitt (WDW) equation and
see whether the solutions to the WDW equation satisfy the DeWitt boundary
condition. We find that by using a suitable Born-Oppenheimer (BO)
approximation, whose validity is proven, the DeWitt condition is satisfied.
Therefore, the big rip singularity is expected to be avoided in the quantum
realm.
