Quantum cosmology of Eddington-Born-Infeld gravity fed by a scalar field: the big rip case

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.